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mal Wurzel aus 2.","middle",{"stem":588,"formulaId":589,"title":590,"latex":591,"latexHtml":592,"conditionsHtml":593,"figureHtml":594,"figureCaption":595,"variables":596,"summary":604,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fdiagonale-rechteck","rectangle-diagonal","Diagonale eines Rechtecks","d = \\sqrt{a^2 + b^2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>d\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d = \\sqrt{a^2 + 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Die Diagonale eines Rechtecks ist die Wurzel aus der Summe der Quadrate von Länge und Breite.",{"stem":606,"formulaId":607,"title":608,"latex":609,"latexHtml":610,"conditionsHtml":611,"figureHtml":612,"figureCaption":613,"variables":614,"summary":627,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Faehnliche-figuren","similarity-ratio","Flächen- und Volumenverhältnis ähnlicher Figuren","A' = k^2 \\cdot A,\\quad V' = k^3 \\cdot V","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmsup>\u003Cmi>V\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>k\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A' = k^2 \\cdot A,\\quad V' = k^3 \\cdot V\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8019em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9963em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8019em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 148.8\" width=\"288\" height=\"148.8\" role=\"img\" aria-label=\"Dreieck mit dem Flächeninhalt A und ähnliches Bilddreieck mit doppelt so langen Seiten (k = 2) und dem Flächeninhalt A'\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-similarity-ratio-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-similarity-ratio-clip\">\u003Crect x=\"0\" y=\"0\" width=\"288\" height=\"148.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"19.2,124.8 91.2,124.8 43.2,72\" class=\"fig-muted\"\u002F>\u003Cpolygon points=\"134.4,124.8 278.4,124.8 182.4,19.2\" class=\"fig-main fig-fill\"\u002F>\u003Ctext x=\"51.36\" y=\"107.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ctext x=\"198.24\" y=\"89.76\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A'\u003C\u002Ftext>\u003C\u002Fsvg>","Dreieck mit dem Flächeninhalt A und ähnliches Bilddreieck mit doppelt so langen Seiten (k = 2) und dem Flächeninhalt A'",[615,619,623],{"symbol":616,"meaning":617,"symbolHtml":618},"k","Streckfaktor, das Verhältnis entsprechender Längen (Bildlänge durch Originallänge)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":620,"meaning":621,"symbolHtml":622},"A, A'","Flächeninhalt der Originalfigur und der ähnlichen Bildfigur","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A, A'\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9463em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":624,"meaning":625,"symbolHtml":626},"V, V'","Volumen des Originalkörpers und des ähnlichen Bildkörpers","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsup>\u003Cmi>V\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">′\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V, V'\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9463em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7519em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">′\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Werden alle Längen mit k multipliziert, wächst die Fläche mit k² und das Volumen mit k³.",{"stem":629,"formulaId":630,"title":631,"latex":632,"latexHtml":633,"conditionsHtml":593,"figureHtml":634,"figureCaption":635,"variables":636,"summary":649,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-ellipse","ellipse-area","Flächeninhalt einer Ellipse","A = \\pi a b","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\pi a b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">ab\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 278.4 187.2\" width=\"278.4\" height=\"187.2\" role=\"img\" aria-label=\"Ellipse mit den Halbachsen a und b, die Fläche A ist hervorgehoben\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-ellipse-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-ellipse-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"278.4\" height=\"187.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cellipse cx=\"139.2\" cy=\"93.6\" rx=\"124.8\" ry=\"76.8\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"139.2\" y1=\"93.6\" x2=\"264\" y2=\"93.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"139.2\" y1=\"93.6\" x2=\"139.2\" y2=\"16.8\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 151.2 93.6 L 151.2 81.6 L 139.2 81.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"145.2\" cy=\"87.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"201.6\" y=\"108\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"125.76\" y=\"55.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"72\" y=\"120\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"139.2\" cy=\"93.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003C\u002Fsvg>","Ellipse mit den Halbachsen a und b, die Fläche A ist hervorgehoben",[637,641,643,645],{"symbol":638,"meaning":639,"symbolHtml":640},"A","Flächeninhalt der Ellipse","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":582,"meaning":642,"symbolHtml":584},"große Halbachse, halbe Länge der Ellipse",{"symbol":601,"meaning":644,"symbolHtml":603},"kleine Halbachse, halbe Breite der Ellipse",{"symbol":646,"meaning":647,"symbolHtml":648},"\\pi","Kreiszahl, etwa 3,14159","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>π\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\pi\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Eine Ellipse mit den Halbachsen a und b hat den Flächeninhalt π mal a mal b.","upper",{"stem":652,"formulaId":653,"title":654,"latex":655,"latexHtml":656,"conditionsHtml":553,"figureHtml":657,"figureCaption":658,"variables":659,"summary":666,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-raute","rhombus-area","Flächeninhalt einer Raute","A = \\frac{1}{2} \\cdot e \\cdot f","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>e\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{1}{2} \\cdot e \\cdot f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4445em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 201.6 240\" width=\"201.6\" height=\"240\" role=\"img\" aria-label=\"Raute mit den beiden Diagonalen e und f, die sich rechtwinklig schneiden\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-rhombus-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-rhombus-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"201.6\" height=\"240\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,120 100.8,216 172.8,120 100.8,24\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"28.8\" y1=\"120\" x2=\"172.8\" y2=\"120\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"100.8\" y1=\"216\" x2=\"100.8\" y2=\"24\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 112.8 120 L 112.8 108 L 100.8 108\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"106.8\" cy=\"114\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"64.8\" y=\"134.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">e\u003C\u002Ftext>\u003Ctext x=\"88.8\" y=\"172.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003C\u002Fsvg>","Raute mit den beiden Diagonalen e und f, die sich rechtwinklig schneiden",[660,662],{"symbol":638,"meaning":661,"symbolHtml":640},"Flächeninhalt",{"symbol":663,"meaning":664,"symbolHtml":665},"e, f","Längen der beiden Diagonalen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e, f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Der Flächeninhalt einer Raute ist das halbe Produkt ihrer beiden Diagonalen.",{"stem":668,"formulaId":669,"title":670,"latex":655,"latexHtml":656,"conditionsHtml":553,"figureHtml":671,"figureCaption":672,"variables":673,"summary":677,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-drachenviereck","kite-area","Flächeninhalt eines Drachenvierecks","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 201.6 240\" width=\"201.6\" height=\"240\" role=\"img\" aria-label=\"Drachenviereck mit den senkrecht aufeinander stehenden Diagonalen e und f\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-kite-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-kite-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"201.6\" height=\"240\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"100.8,216 172.8,81.6 100.8,24 28.8,81.6\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"100.8\" y1=\"216\" x2=\"100.8\" y2=\"24\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"28.8\" y1=\"81.6\" x2=\"172.8\" y2=\"81.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 112.8 81.6 L 112.8 93.6 L 100.8 93.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"106.8\" cy=\"87.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"88.8\" y=\"153.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">e\u003C\u002Ftext>\u003Ctext x=\"64.8\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003C\u002Fsvg>","Drachenviereck mit den senkrecht aufeinander stehenden Diagonalen e und f",[674,675],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":663,"meaning":676,"symbolHtml":665},"Längen der beiden Diagonalen, die senkrecht aufeinander stehen","Der Flächeninhalt eines Drachenvierecks ist das halbe Produkt seiner beiden Diagonalen.",{"stem":679,"formulaId":680,"title":681,"latex":682,"latexHtml":683,"conditionsHtml":553,"figureHtml":684,"figureCaption":685,"variables":686,"summary":696,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-dreieck","triangle-area","Flächeninhalt eines Dreiecks","A = \\frac{1}{2} \\cdot g \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>g\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{1}{2} \\cdot g \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 196.8\" width=\"288\" height=\"196.8\" role=\"img\" aria-label=\"Dreieck mit der Grundseite g und der zugehörigen Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-triangle-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-triangle-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"288\" height=\"196.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,163.2 264,163.2 110.4,19.2\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"110.4\" y1=\"19.2\" x2=\"110.4\" y2=\"163.2\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 122.4 163.2 L 122.4 151.2 L 110.4 151.2\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"116.4\" cy=\"157.2\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"177.6\" y=\"180\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">g\u003C\u002Ftext>\u003Ctext x=\"122.4\" y=\"100.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","Dreieck mit der Grundseite g und der zugehörigen Höhe h",[687,688,692],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":689,"meaning":690,"symbolHtml":691},"g","Grundseite, eine beliebige Seite des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>g\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">g\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":693,"meaning":694,"symbolHtml":695},"h","Höhe, der senkrechte Abstand der gegenüberliegenden Ecke von der Grundseite","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Der Flächeninhalt eines Dreiecks ist die Hälfte von Grundseite mal zugehöriger Höhe.",{"stem":698,"formulaId":699,"title":700,"latex":701,"latexHtml":702,"conditionsHtml":573,"figureHtml":703,"figureCaption":704,"variables":705,"summary":710,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-gleichseitiges-dreieck","equilateral-triangle-area","Flächeninhalt eines gleichseitigen Dreiecks","A = \\frac{a^2}{4} \\sqrt{3}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmsqrt>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{a^2}{4} \\sqrt{3}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1771em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9561em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9161em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.0839em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 220.8\" width=\"249.6\" height=\"220.8\" role=\"img\" aria-label=\"Gleichseitiges Dreieck mit der Seitenlänge a und dem Flächeninhalt A\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-equilateral-triangle-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-equilateral-triangle-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"220.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,187.2 220.8,187.2 124.8,20.93\" class=\"fig-main fig-fill\"\u002F>\u003Ctext x=\"124.8\" y=\"204\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"62.4\" y=\"93.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"187.2\" y=\"93.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"124.8\" y=\"132\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003C\u002Fsvg>","Gleichseitiges Dreieck mit der Seitenlänge a und dem Flächeninhalt A",[706,708],{"symbol":638,"meaning":707,"symbolHtml":640},"Flächeninhalt des Dreiecks",{"symbol":582,"meaning":709,"symbolHtml":584},"Seitenlänge des gleichseitigen Dreiecks","Ein gleichseitiges Dreieck mit Seite a hat den Flächeninhalt a² geteilt durch 4 mal Wurzel aus 3.",{"stem":712,"formulaId":713,"title":714,"latex":715,"latexHtml":716,"conditionsHtml":553,"figureHtml":717,"figureCaption":718,"variables":719,"summary":728,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-kreis","circle-area","Flächeninhalt eines Kreises","A = \\pi r^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\pi r^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 249.6\" width=\"249.6\" height=\"249.6\" role=\"img\" aria-label=\"Kreis mit Mittelpunkt M und Radius r, die Kreisfläche A ist hervorgehoben\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-circle-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-circle-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"249.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cellipse cx=\"124.8\" cy=\"124.8\" rx=\"105.6\" ry=\"105.6\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"230.4\" y2=\"124.8\" class=\"fig-main\"\u002F>\u003Ctext x=\"177.6\" y=\"110.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"88.8\" y=\"84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreis mit Mittelpunkt M und Radius r, die Kreisfläche A ist hervorgehoben",[720,722,726],{"symbol":638,"meaning":721,"symbolHtml":640},"Flächeninhalt des Kreises",{"symbol":723,"meaning":724,"symbolHtml":725},"r","Radius, der Abstand vom Mittelpunkt zum Rand","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":646,"meaning":727,"symbolHtml":648},"Kreiszahl, ungefähr 3,14159","Der Flächeninhalt eines Kreises ist π mal Radius zum Quadrat.",{"stem":730,"formulaId":731,"title":732,"latex":733,"latexHtml":734,"conditionsHtml":735,"figureHtml":736,"figureCaption":737,"variables":738,"summary":750,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisring","annulus-area","Flächeninhalt eines Kreisrings","A = \\pi \\left(r_a^2 - r_i^2\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\pi \\left(r_a^2 - r_i^2\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2141em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>>\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_a > r_i \\geq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6891em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.786em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 249.6\" width=\"249.6\" height=\"249.6\" role=\"img\" aria-label=\"Kreisring zwischen dem äußeren Kreis mit 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80.02,80.02 84.1,76.27 88.46,72.91 93.12,69.94 98.02,67.39 103.15,65.28 108.38,63.6 113.81,62.4 119.28,61.68 124.8,61.44 130.32,61.68 135.79,62.4 141.22,63.6 146.45,65.28 151.58,67.39 156.48,69.94 161.14,72.91 165.5,76.27 169.58,80.02 173.33,84.1 176.69,88.46 179.66,93.12 182.21,98.02 184.32,103.15 186,108.38 187.2,113.81 187.92,119.28 188.16,124.8\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"230.4\" y2=\"124.8\" class=\"fig-main\"\u002F>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"80.02\" y2=\"80.02\" class=\"fig-main\"\u002F>\u003Ctext x=\"209.28\" y=\"99.84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003Ctspan class=\"fig-sub\" dy=\"4\">a\u003C\u002Ftspan>\u003C\u002Ftext>\u003Ctext x=\"110.4\" y=\"88.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003Ctspan class=\"fig-sub\" dy=\"4\">i\u003C\u002Ftspan>\u003C\u002Ftext>\u003Ctext x=\"76.37\" y=\"194.02\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreisring zwischen dem äußeren Kreis mit Radius rₐ und dem inneren Kreis mit Radius rᵢ",[739,741,745,749],{"symbol":638,"meaning":740,"symbolHtml":640},"Flächeninhalt des Kreisrings",{"symbol":742,"meaning":743,"symbolHtml":744},"r_a","Radius des äußeren Kreises","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":746,"meaning":747,"symbolHtml":748},"r_i","Radius des inneren Kreises (des Lochs)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":646,"meaning":647,"symbolHtml":648},"Die Fläche eines Kreisrings ist die Fläche des äußeren Kreises minus die Fläche des inneren Kreises.",{"stem":752,"formulaId":753,"title":754,"latex":755,"latexHtml":756,"conditionsHtml":757,"figureHtml":758,"figureCaption":759,"variables":760,"summary":769,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreissegment","circular-segment-area","Flächeninhalt eines Kreissegments","A = \\frac{r^2}{2} \\left(\\alpha - \\sin \\alpha\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{r^2}{2} \\left(\\alpha - \\sin \\alpha\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1771em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo><\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 < \\alpha < 2\\pi,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6835em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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Bogenmaß\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 249.6\" width=\"249.6\" height=\"249.6\" role=\"img\" aria-label=\"Kreissegment A zwischen Sehne und Kreisbogen, mit Mittelpunktswinkel α und Radius r\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-circular-segment-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-circular-segment-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"249.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"105.6\" class=\"fig-muted\"\u002F>\u003Cpolygon points=\"205.68,56.93 203.28,54.14 200.78,51.46 198.14,48.82 195.46,46.32 192.67,43.92 189.79,41.57 186.86,39.36 183.84,37.25 180.77,35.23 177.6,33.36 174.38,31.58 171.07,29.9 167.76,28.32 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class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"124.8\" y=\"39.36\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreissegment A zwischen Sehne und Kreisbogen, mit Mittelpunktswinkel α und Radius r",[761,763,765],{"symbol":638,"meaning":762,"symbolHtml":640},"Flächeninhalt des Kreissegments",{"symbol":723,"meaning":764,"symbolHtml":725},"Radius des Kreises",{"symbol":766,"meaning":767,"symbolHtml":768},"\\alpha","Mittelpunktswinkel über der Sehne, im Bogenmaß","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Ein Kreissegment ist die Fläche zwischen Sehne und Bogen; sie ist der Kreissektor minus das Dreieck zum Mittelpunkt.",{"stem":771,"formulaId":772,"title":773,"latex":774,"latexHtml":775,"conditionsHtml":776,"figureHtml":777,"figureCaption":778,"variables":779,"summary":786,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreissektor","circular-sector-area","Flächeninhalt eines Kreissektors","A = \\frac{\\alpha}{360^\\circ} \\cdot \\pi r^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>α\u003C\u002Fmi>\u003Cmsup>\u003Cmn>360\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{\\alpha}{360^\\circ} \\cdot \\pi r^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">36\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6001em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo><\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmsup>\u003Cmn>360\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0^\\circ < \\alpha \\leq 360^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7132em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6741em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">36\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 249.6\" width=\"249.6\" height=\"249.6\" role=\"img\" aria-label=\"Kreissektor mit Mittelpunktswinkel α und Radius r\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-circular-sector-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-circular-sector-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"249.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"105.6\" class=\"fig-muted\"\u002F>\u003Cpath d=\"M 124.8 124.8 L 226.8 97.47 A 105.6 105.6 0 0 0 80.17 29.09 Z\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 124.8 124.8 L 146.05 119.11 A 22 22 0 0 0 115.5 104.86 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"139.17\" y=\"93.99\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Ctext x=\"180\" y=\"127.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"154.56\" y=\"57.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreissektor mit Mittelpunktswinkel α und Radius r",[780,782,784,785],{"symbol":638,"meaning":781,"symbolHtml":640},"Flächeninhalt des Kreissektors",{"symbol":766,"meaning":783,"symbolHtml":768},"Mittelpunktswinkel in Grad",{"symbol":723,"meaning":764,"symbolHtml":725},{"symbol":646,"meaning":727,"symbolHtml":648},"Ein Kreissektor ist der Anteil α\u002F360° von der ganzen Kreisfläche πr².",{"stem":788,"formulaId":789,"title":790,"latex":791,"latexHtml":792,"conditionsHtml":553,"figureHtml":793,"figureCaption":794,"variables":795,"summary":801,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-parallelogramm","parallelogram-area","Flächeninhalt eines Parallelogramms","A = g \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>g\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = g \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 299.2 167.2\" width=\"299.2\" height=\"167.2\" role=\"img\" aria-label=\"Parallelogramm mit der Grundseite g und der zugehörigen Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-parallelogram-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-parallelogram-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"299.2\" height=\"167.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"22,136.4 220,136.4 277.2,22 79.2,22\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"79.2\" y1=\"22\" x2=\"79.2\" y2=\"136.4\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 91.2 136.4 L 91.2 124.4 L 79.2 124.4\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"85.2\" cy=\"130.4\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"149.6\" y=\"151.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">g\u003C\u002Ftext>\u003Ctext x=\"90.2\" y=\"79.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","Parallelogramm mit der Grundseite g und der zugehörigen Höhe h",[796,797,799],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":689,"meaning":798,"symbolHtml":691},"Grundseite, eine Seite des Parallelogramms",{"symbol":693,"meaning":800,"symbolHtml":695},"Höhe, der senkrechte Abstand zwischen der Grundseite und der gegenüberliegenden Seite","Der Flächeninhalt eines Parallelogramms ist Grundseite mal zugehöriger Höhe.",{"stem":803,"formulaId":804,"title":805,"latex":806,"latexHtml":807,"conditionsHtml":553,"figureHtml":808,"figureCaption":809,"variables":810,"summary":813,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-quadrat","square-area","Flächeninhalt eines Quadrats","A = a^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = a^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 201.6 201.6\" width=\"201.6\" height=\"201.6\" role=\"img\" aria-label=\"Quadrat mit der Seitenlänge a und dem Flächeninhalt A\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-square-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-square-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"201.6\" height=\"201.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"33.6,168 177.6,168 177.6,24 33.6,24\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 45.6 168 L 45.6 156 L 33.6 156\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"39.6\" cy=\"162\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"105.6\" y=\"184.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"16.8\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"105.6\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003C\u002Fsvg>","Quadrat mit der Seitenlänge a und dem Flächeninhalt A",[811,812],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":582,"meaning":583,"symbolHtml":584},"Der Flächeninhalt eines Quadrats ist die Seitenlänge mal sich selbst.",{"stem":815,"formulaId":816,"title":817,"latex":818,"latexHtml":819,"conditionsHtml":553,"figureHtml":820,"figureCaption":821,"variables":822,"summary":826,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-rechteck","rectangle-area","Flächeninhalt eines Rechtecks","A = a \\cdot b","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = a \\cdot b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-rectangle-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"297.6\" height=\"196.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"33.6,163.2 273.6,163.2 273.6,19.2 33.6,19.2\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 45.6 163.2 L 45.6 151.2 L 33.6 151.2\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"39.6\" cy=\"157.2\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"153.6\" y=\"180\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"288\" y=\"91.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"153.6\" y=\"91.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003C\u002Fsvg>","Rechteck mit der Länge a, der Breite b und dem Flächeninhalt A",[823,824,825],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":582,"meaning":599,"symbolHtml":584},{"symbol":601,"meaning":602,"symbolHtml":603},"Der Flächeninhalt eines Rechtecks ist Länge mal Breite.",{"stem":828,"formulaId":829,"title":830,"latex":831,"latexHtml":832,"conditionsHtml":833,"figureHtml":834,"figureCaption":835,"variables":836,"summary":844,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-regelmaessiges-vieleck","regular-polygon-area","Flächeninhalt eines regelmäßigen n-Ecks","A = \\frac{n \\cdot a^2}{4 \\cdot \\tan\\left(\\frac{180^\\circ}{n}\\right)}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmrow>\u003Cmn>4\u003C\u002Fmn>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>tan\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{n \\cdot a^2}{4 \\cdot \\tan\\left(\\frac{180^\\circ}{n}\\right)}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.5811em;vertical-align:-1.09em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.26em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">18\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6035em;\">\u003Cspan style=\"top:-2.786em;margin-right:0.0714em;\">\u003Cspan class=\"pstrut\" style=\"height:2.5em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size3 size1 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.345em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.09em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\ge 3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 240 235.2\" width=\"240\" height=\"235.2\" role=\"img\" aria-label=\"Regelmäßiges Fünfeck (n = 5) mit der Seitenlänge a, vom Mittelpunkt aus in n gleiche Dreiecke zerlegt\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-regular-polygon-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-regular-polygon-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"240\" height=\"235.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"120,24 28.7,90.34 63.55,197.66 176.45,197.66 211.3,90.34\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"120\" y2=\"24\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"28.7\" y2=\"90.34\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"63.55\" y2=\"197.66\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"176.45\" y2=\"197.66\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"211.3\" y2=\"90.34\" class=\"fig-dashed\"\u002F>\u003Ccircle cx=\"120\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"120\" y=\"213.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003C\u002Fsvg>","Regelmäßiges Fünfeck (n = 5) mit der Seitenlänge a, vom Mittelpunkt aus in n gleiche Dreiecke zerlegt",[837,838,842],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":839,"meaning":840,"symbolHtml":841},"n","Anzahl der Ecken (und Seiten)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":582,"meaning":843,"symbolHtml":584},"Seitenlänge","Ein regelmäßiges n-Eck mit der Seitenlänge a zerfällt in n gleiche Dreiecke; daraus folgt seine Fläche.",{"stem":846,"formulaId":847,"title":848,"latex":849,"latexHtml":850,"conditionsHtml":573,"figureHtml":851,"figureCaption":852,"variables":853,"summary":858,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-sechseck","regular-hexagon-area","Flächeninhalt eines regelmäßigen Sechsecks","A = \\frac{3}{2} a^2 \\sqrt{3}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>3\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmsqrt>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{3}{2} a^2 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style=\"height:0.0839em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 240 220.8\" width=\"240\" height=\"220.8\" role=\"img\" aria-label=\"Regelmäßiges Sechseck mit der Seitenlänge a, zerlegt in sechs gleichseitige Dreiecke\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-regular-hexagon-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-regular-hexagon-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"240\" height=\"220.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"216,110.4 168,27.26 72,27.26 24,110.4 72,193.54 168,193.54\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"24\" y1=\"110.4\" x2=\"216\" y2=\"110.4\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"72\" y1=\"27.26\" x2=\"168\" y2=\"193.54\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"168\" y1=\"27.26\" x2=\"72\" y2=\"193.54\" class=\"fig-dashed\"\u002F>\u003Ctext x=\"120\" y=\"208.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"168\" y=\"98.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003C\u002Fsvg>","Regelmäßiges Sechseck mit der Seitenlänge a, zerlegt in sechs gleichseitige Dreiecke",[854,856],{"symbol":638,"meaning":855,"symbolHtml":640},"Flächeninhalt des Sechsecks",{"symbol":582,"meaning":857,"symbolHtml":584},"Seitenlänge des regelmäßigen Sechsecks","Ein regelmäßiges Sechseck besteht aus sechs gleichseitigen Dreiecken, seine Fläche ist 3\u002F2 · a² · √3.",{"stem":860,"formulaId":861,"title":862,"latex":863,"latexHtml":864,"conditionsHtml":553,"figureHtml":865,"figureCaption":866,"variables":867,"summary":875,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-trapez","trapezoid-area","Flächeninhalt eines Trapezes","A = \\frac{1}{2} \\cdot (a + c) \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\frac{1}{2} \\cdot (a + c) \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan 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class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 192\" width=\"288\" height=\"192\" role=\"img\" aria-label=\"Trapez mit den parallelen Seiten a und c und der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-trapezoid-area-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-trapezoid-area-clip\">\u003Crect x=\"0\" y=\"0\" width=\"288\" height=\"192\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,158.4 264,158.4 201.6,33.6 96,33.6\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"96\" y1=\"33.6\" x2=\"96\" y2=\"158.4\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 108 158.4 L 108 146.4 L 96 146.4\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"102\" cy=\"152.4\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"144\" y=\"175.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"148.8\" y=\"16.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ctext x=\"108\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","Trapez mit den parallelen Seiten a und c und der Höhe h",[868,869,873],{"symbol":638,"meaning":661,"symbolHtml":640},{"symbol":870,"meaning":871,"symbolHtml":872},"a, c","die beiden parallelen Seiten des Trapezes","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":693,"meaning":874,"symbolHtml":695},"Höhe, der senkrechte Abstand zwischen den parallelen Seiten","Der Flächeninhalt eines Trapezes ist der Mittelwert der parallelen Seiten mal der Höhe.",{"stem":877,"formulaId":878,"title":879,"latex":880,"latexHtml":881,"conditionsHtml":573,"figureHtml":882,"figureCaption":883,"variables":884,"summary":888,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fhoehe-gleichseitiges-dreieck","equilateral-triangle-height","Höhe im gleichseitigen Dreieck","h = \\frac{a}{2} \\sqrt{3}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmsqrt>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h = \\frac{a}{2} \\sqrt{3}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9561em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>h\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>q\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h^2 = p \\cdot q\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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class=\"fig-dot\"\u002F>\u003Ctext x=\"105.6\" y=\"160.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">q\u003C\u002Ftext>\u003Ctext x=\"225.6\" y=\"160.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">p\u003C\u002Ftext>\u003Ctext x=\"192.96\" y=\"91.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"240.96\" y=\"74.88\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"94.08\" y=\"71.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ccircle cx=\"28.8\" cy=\"144\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"10.8\" y=\"148\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"268.8\" cy=\"144\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"276.8\" y=\"148\" text-anchor=\"start\" 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class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":906,"meaning":907,"symbolHtml":908},"q","an der Kathete b anliegender Hypotenusenabschnitt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>q\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">q\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":910,"meaning":911,"symbolHtml":912},"\\gamma","Winkel bei C, gegenüber der Hypotenuse c","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Im rechtwinkligen Dreieck ist das Quadrat der Höhe gleich dem Produkt der beiden Hypotenusenabschnitte.",{"stem":915,"formulaId":916,"title":917,"latex":918,"latexHtml":919,"conditionsHtml":553,"figureHtml":920,"figureCaption":921,"variables":922,"summary":934,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Finkreisradius","incircle-radius","Inkreisradius eines Dreiecks","r = \\frac{A}{s}, \\quad s = \\frac{a + b + c}{2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r = \\frac{A}{s}, \\quad s = \\frac{a + b + c}{2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0463em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Der Radius des Inkreises ist der Flächeninhalt des Dreiecks geteilt durch den halben Umfang.",{"stem":936,"formulaId":937,"title":938,"latex":939,"latexHtml":940,"conditionsHtml":941,"figureHtml":942,"figureCaption":943,"variables":944,"summary":951,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Finnenwinkelsumme-vieleck","polygon-angle-sum","Innenwinkelsumme im Vieleck","S = (n - 2) \\cdot 180^\\circ","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo 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class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7241em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 220.8\" width=\"288\" height=\"220.8\" role=\"img\" aria-label=\"Fünfeck (n = 5), von einer Ecke aus durch Diagonalen in n − 2 = 3 Dreiecke zerlegt\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-polygon-angle-sum-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" 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cy=\"28.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"176.4\" y=\"14.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","Rechtwinkliges Dreieck mit der Hypotenuse c, der Kathete a und dem an a anliegenden Hypotenusenabschnitt p",[961,963,967,968],{"symbol":582,"meaning":962,"symbolHtml":584},"Kathete, eine Seite am rechten Winkel",{"symbol":964,"meaning":965,"symbolHtml":966},"c","Hypotenuse, die Seite gegenüber dem rechten Winkel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":902,"meaning":903,"symbolHtml":904},{"symbol":910,"meaning":911,"symbolHtml":912},"Im rechtwinkligen Dreieck ist das Kathetenquadrat gleich Hypotenuse mal anliegendem Hypotenusenabschnitt.",{"stem":971,"formulaId":972,"title":973,"latex":974,"latexHtml":975,"conditionsHtml":976,"figureHtml":977,"figureCaption":978,"variables":979,"summary":989,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisgleichung","circle-equation","Kreisgleichung","(x - x_M)^2 + (y - y_M)^2 = r^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>y\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(x - x_M)^2 + (y - y_M)^2 = r^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1141em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan 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style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 252 252\" width=\"252\" height=\"252\" role=\"img\" aria-label=\"Kreis um M(2 | −1) mit Radius 3; für einen Punkt P(x | y) auf dem Kreis bilden die waagerechte und die senkrechte Abstandsstrecke zu M und r ein rechtwinkliges Dreieck\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-circle-equation-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" 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y\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":985,"meaning":986,"symbolHtml":987},"x_M, y_M","Koordinaten des Mittelpunkts M(x_M | y_M)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_M, y_M\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":723,"meaning":764,"symbolHtml":725},"Ein Punkt (x | y) liegt genau dann auf dem Kreis um M mit Radius r, wenn sein Abstand zu M gleich r ist.",{"stem":991,"formulaId":992,"title":993,"latex":994,"latexHtml":995,"conditionsHtml":996,"figureHtml":997,"figureCaption":998,"variables":999,"summary":1012,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkugelkappe","spherical-cap","Kugelkappe und Kugelsegment","V = \\frac{\\pi h^2}{3} (3r - h), \\qquad M = 2 \\pi r h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>h\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>M\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{\\pi h^2}{3} (3r - h), \\qquad M = 2 \\pi r h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1771em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo><\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 < h \\le 2r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6835em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 235.2 235.2\" width=\"235.2\" height=\"235.2\" role=\"img\" aria-label=\"Kugel mit Radius r; eine Ebene schneidet das Kugelsegment der Höhe h ab, seine gewölbte Fläche ist die Kugelkappe\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-spherical-cap-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-spherical-cap-clip\">\u003Crect x=\"0\" y=\"0\" width=\"235.2\" height=\"235.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"117.6\" cy=\"117.6\" r=\"96\" class=\"fig-muted\"\u002F>\u003Cpolygon points=\"205.58,79.2 199.1,66.91 190.94,55.68 181.25,45.7 170.16,37.3 158.02,30.53 145.06,25.58 131.47,22.61 117.6,21.6 103.73,22.61 90.14,25.58 77.18,30.53 65.04,37.3 53.95,45.7 44.26,55.68 36.1,66.91 29.62,79.2 29.62,79.2 31.3,83.9 36.34,88.37 44.45,92.54 55.39,96.19 68.74,99.17 83.95,101.38 100.42,102.72 117.6,103.2 134.78,102.72 151.25,101.38 166.46,99.17 179.81,96.19 190.75,92.54 198.86,88.37 203.9,83.9 205.58,79.2\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 205.59 79.2 A 96 96 0 0 0 29.61 79.2\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 205.58 79.2 A 87.98 24 0 0 0 29.62 79.2\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 29.62 79.2 A 87.98 24 0 0 0 205.58 79.2\" class=\"fig-main\"\u002F>\u003Cline x1=\"117.6\" y1=\"79.2\" x2=\"117.6\" y2=\"21.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"117.6\" y1=\"117.6\" x2=\"21.6\" y2=\"117.6\" class=\"fig-muted\"\u002F>\u003Ccircle cx=\"117.6\" cy=\"117.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"111.6\" y=\"133.6\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003Ctext x=\"129.6\" y=\"50.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"69.6\" y=\"129.12\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003C\u002Fsvg>","Kugel mit Radius r; eine Ebene schneidet das Kugelsegment der Höhe h ab, seine gewölbte Fläche ist die Kugelkappe",[1000,1004,1008,1010],{"symbol":1001,"meaning":1002,"symbolHtml":1003},"V","Volumen des Kugelsegments","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1005,"meaning":1006,"symbolHtml":1007},"M","Flächeninhalt der gewölbten Fläche (Kugelkappe), ohne Grundkreis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>M\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">M\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">M\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":723,"meaning":1009,"symbolHtml":725},"Radius der Kugel",{"symbol":693,"meaning":1011,"symbolHtml":695},"Höhe des Segments, vom Grundkreis bis zum Pol","Volumen und gewölbte Fläche eines Stücks, das eine Ebene von einer Kugel abschneidet.",{"stem":1014,"formulaId":1015,"title":1016,"latex":1017,"latexHtml":1018,"conditionsHtml":776,"figureHtml":1019,"figureCaption":1020,"variables":1021,"summary":1027,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisbogen","arc-length","Länge eines Kreisbogens","b = \\frac{\\alpha}{360^\\circ} \\cdot 2 \\pi r","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>α\u003C\u002Fmi>\u003Cmsup>\u003Cmn>360\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b = \\frac{\\alpha}{360^\\circ} \\cdot 2 \\pi r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">36\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6001em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 261.6\" width=\"249.6\" height=\"261.6\" role=\"img\" aria-label=\"Kreisbogen b zum Mittelpunktswinkel α in einem Kreis mit Radius r\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-arc-length-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-arc-length-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"261.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"124.8\" cy=\"136.8\" r=\"105.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"124.8\" y1=\"136.8\" x2=\"224.02\" y2=\"100.7\" class=\"fig-muted\"\u002F>\u003Cline x1=\"124.8\" y1=\"136.8\" x2=\"72\" y2=\"45.36\" class=\"fig-muted\"\u002F>\u003Cpath d=\"M 224.03 100.68 A 105.6 105.6 0 0 0 72 45.35\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 124.8 136.8 L 145.47 129.28 A 22 22 0 0 0 113.8 117.75 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"136.43\" y=\"104.85\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Ctext x=\"179.04\" y=\"132\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"166.66\" y=\"21.79\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"136.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"152.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreisbogen b zum Mittelpunktswinkel α in einem Kreis mit Radius r",[1022,1024,1025,1026],{"symbol":601,"meaning":1023,"symbolHtml":603},"Länge des Kreisbogens",{"symbol":766,"meaning":783,"symbolHtml":768},{"symbol":723,"meaning":764,"symbolHtml":725},{"symbol":646,"meaning":727,"symbolHtml":648},"Ein Kreisbogen ist der Anteil α\u002F360° vom ganzen Kreisumfang 2πr.",{"stem":1029,"formulaId":1030,"title":1031,"latex":1032,"latexHtml":1033,"conditionsHtml":553,"figureHtml":1034,"figureCaption":1035,"variables":1036,"summary":1043,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kugel","sphere-surface","Oberfläche einer Kugel","O = 4 \\pi r^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>4\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation 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class=\"fig-label\">O\u003C\u002Ftext>\u003C\u002Fsvg>","Kugel mit dem Mittelpunkt M und dem Radius r; die Oberfläche O ist die gewölbte Hülle",[1037,1041,1042],{"symbol":1038,"meaning":1039,"symbolHtml":1040},"O","Oberflächeninhalt der Kugel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">O\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":723,"meaning":1009,"symbolHtml":725},{"symbol":646,"meaning":727,"symbolHtml":648},"Die Oberfläche einer Kugel ist viermal so groß wie die Fläche ihres größten Querschnittskreises.",{"stem":1045,"formulaId":1046,"title":1047,"latex":1048,"latexHtml":1049,"conditionsHtml":1050,"figureHtml":1051,"figureCaption":1052,"variables":1053,"summary":1062,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-pyramide","pyramid-surface","Oberfläche einer quadratischen Pyramide","O = a^2 + 2 a h_s","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003Cmsub>\u003Cmi>h\u003C\u002Fmi>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O = a^2 + 2 a h_s\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">O\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan 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style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>h\u003C\u002Fmi>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>>\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h_s > \\frac{a}{2},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0404em;vertical-align:-0.345em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6954em;\">\u003Cspan style=\"top:-2.655em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.394em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan 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z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-cone-surface-clip\">\u003Crect x=\"0\" y=\"0\" width=\"228.8\" height=\"223.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"111.8,23.4 24.7,174.88 23.4,179.5 24.8,184.08 28.81,188.55 35.36,192.71 44.2,196.51 55.07,199.73 67.7,202.38 81.64,204.31 96.46,205.5 111.8,205.92 127.14,205.5 141.96,204.31 155.9,202.38 168.53,199.73 179.4,196.51 188.24,192.71 194.79,188.55 198.8,184.08 200.2,179.5 198.9,174.88\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 198.91 174.89 A 88.4 26.52 0 0 0 24.69 174.89\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24.69 174.89 A 88.4 26.52 0 1 0 198.91 174.89\" class=\"fig-main\"\u002F>\u003Cline x1=\"24.7\" y1=\"174.88\" x2=\"111.8\" y2=\"23.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"198.9\" y1=\"174.88\" x2=\"111.8\" y2=\"23.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"111.8\" y1=\"179.4\" x2=\"200.2\" y2=\"179.4\" class=\"fig-main\"\u002F>\u003Ccircle 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πrs.",{"stem":1081,"formulaId":1082,"title":1083,"latex":1084,"latexHtml":1085,"conditionsHtml":1086,"figureHtml":1087,"figureCaption":1088,"variables":1089,"summary":1102,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf","cone-frustum-surface","Oberfläche eines Kegelstumpfs","\\begin{gathered} O = \\pi \\left(R^2 + r^2 + (R + r)\\, s\\right) \\\\ s = \\sqrt{(R - r)^2 + h^2} \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmrow>\u003Cmo 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class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.184em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R > r > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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62.4,36\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 196.8 141.6 A 86.4 25.92 0 0 0 24 141.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24 141.6 A 86.4 25.92 0 0 0 196.8 141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"24\" y1=\"141.6\" x2=\"62.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"196.8\" y1=\"141.6\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cellipse cx=\"110.4\" cy=\"36\" rx=\"48\" ry=\"14.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"196.8\" y2=\"141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"36\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"110.4\" y2=\"36\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 110.4 129.6 L 122.4 129.6 L 122.4 141.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"116.4\" cy=\"135.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"141.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"36\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"153.6\" y=\"153.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">R\u003C\u002Ftext>\u003Ctext x=\"172.8\" y=\"24\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"98.4\" y=\"88.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"192.96\" y=\"86.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">s\u003C\u002Ftext>\u003C\u002Fsvg>","Kegelstumpf mit den Radien R und r, der Höhe h und der Mantellinie s",[1090,1092,1096,1098,1100],{"symbol":1038,"meaning":1091,"symbolHtml":1040},"Oberfläche (Grundkreis, Deckkreis und Mantel)",{"symbol":1093,"meaning":1094,"symbolHtml":1095},"R","Radius des Grundkreises","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":723,"meaning":1097,"symbolHtml":725},"Radius des Deckkreises",{"symbol":927,"meaning":1099,"symbolHtml":929},"Mantellinie, die schräge Seitenlänge",{"symbol":693,"meaning":1101,"symbolHtml":695},"Höhe des Stumpfs","Die Oberfläche eines Kegelstumpfs besteht aus zwei Kreisen und dem Mantel π(R + r)s.",{"stem":1104,"formulaId":1105,"title":1106,"latex":1107,"latexHtml":1108,"conditionsHtml":1109,"figureHtml":1110,"figureCaption":1111,"variables":1112,"summary":1125,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-prisma","prism-surface","Oberfläche eines Prismas","O = 2 \\cdot G + u \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O = 2 \\cdot G + u \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">O\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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viewBox=\"0 0 206.4 201.6\" width=\"206.4\" height=\"201.6\" role=\"img\" aria-label=\"Gerades Dreiecksprisma: Grund- und Deckfläche G, dazwischen der Mantel aus Rechtecken mit der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-prism-surface-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-prism-surface-clip\">\u003Crect x=\"0\" y=\"0\" width=\"206.4\" height=\"201.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"33.6,172.8 177.6,172.8 153.6,122.4\" class=\"fig-dashed fig-fill\"\u002F>\u003Cpolygon points=\"33.6,172.8 177.6,172.8 177.6,67.2 33.6,67.2\" class=\"fig-muted fig-fill\"\u002F>\u003Cpolygon points=\"33.6,67.2 177.6,67.2 153.6,16.8\" class=\"fig-muted fig-fill\"\u002F>\u003Cline x1=\"33.6\" y1=\"172.8\" x2=\"177.6\" y2=\"172.8\" 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mathnormal\">G\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1120,"meaning":1121,"symbolHtml":1122},"u","Umfang der Grundfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":693,"meaning":1124,"symbolHtml":695},"Höhe des Prismas","Die Oberfläche eines geraden Prismas besteht aus Grund- und Deckfläche und dem Mantel Umfang mal Höhe.",{"stem":1127,"formulaId":1128,"title":1129,"latex":1130,"latexHtml":1131,"conditionsHtml":553,"figureHtml":1132,"figureCaption":1133,"variables":1134,"summary":1143,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-quader","cuboid-surface","Oberfläche eines Quaders","O = 2 \\cdot (ab + ac + bc)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O = 2 \\cdot (ab + ac + bc)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">O\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">ab\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 172.8\" width=\"249.6\" height=\"172.8\" role=\"img\" aria-label=\"Quader mit Länge a, Breite b und Höhe c; die sichtbaren Seitenflächen sind hervorgehoben\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cuboid-surface-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-cuboid-surface-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"172.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon 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x1=\"220.8\" y1=\"21.6\" x2=\"76.8\" y2=\"21.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"28.8\" y2=\"141.6\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"220.8\" y2=\"108\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"76.8\" y1=\"108\" x2=\"76.8\" y2=\"21.6\" class=\"fig-dashed\"\u002F>\u003Ctext x=\"100.8\" y=\"158.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"213.6\" y=\"129.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"14.4\" y=\"98.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003C\u002Fsvg>","Quader mit Länge a, Breite b und Höhe c; die sichtbaren Seitenflächen sind hervorgehoben",[1135,1137,1139,1141],{"symbol":1038,"meaning":1136,"symbolHtml":1040},"Oberflächeninhalt, die Fläche aller sechs Seiten zusammen",{"symbol":582,"meaning":1138,"symbolHtml":584},"Länge des Quaders",{"symbol":601,"meaning":1140,"symbolHtml":603},"Breite des Quaders",{"symbol":964,"meaning":1142,"symbolHtml":966},"Höhe des Quaders","Die Oberfläche eines Quaders ist die Summe seiner sechs Rechtecke, je zwei davon sind gleich.",{"stem":1145,"formulaId":1146,"title":1147,"latex":1148,"latexHtml":1149,"conditionsHtml":553,"figureHtml":1150,"figureCaption":1151,"variables":1152,"summary":1156,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-wuerfel","cube-surface","Oberfläche eines Würfels","O = 6a^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>6\u003C\u002Fmn>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O 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hervorgehoben",[1153,1154],{"symbol":1038,"meaning":1136,"symbolHtml":1040},{"symbol":582,"meaning":1155,"symbolHtml":584},"Kantenlänge des Würfels","Die Oberfläche eines Würfels besteht aus sechs gleichen Quadraten, also 6 mal a².",{"stem":1158,"formulaId":1159,"title":1160,"latex":1161,"latexHtml":1162,"conditionsHtml":553,"figureHtml":1163,"figureCaption":1164,"variables":1165,"summary":1172,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-zylinder","cylinder-surface","Oberfläche eines Zylinders","O = 2 \\pi r^2 + 2 \\pi r h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" 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class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 292.8 259.2\" width=\"292.8\" height=\"259.2\" role=\"img\" aria-label=\"Dreieck mit den drei Seitenlängen a, b und c\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-heron-formula-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-heron-formula-clip\">\u003Crect x=\"0\" y=\"0\" width=\"292.8\" height=\"259.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"28.8,225.6 264,225.6 180,24\" class=\"fig-main fig-fill\"\u002F>\u003Ctext x=\"146.4\" y=\"242.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" 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c",[1210,1211,1213],{"symbol":638,"meaning":707,"symbolHtml":640},{"symbol":931,"meaning":1212,"symbolHtml":933},"die drei Seitenlängen des Dreiecks",{"symbol":927,"meaning":928,"symbolHtml":929},"Der Flächeninhalt eines Dreiecks lässt sich allein aus den drei Seitenlängen über den halben Umfang berechnen.",{"stem":1216,"formulaId":1217,"title":1218,"latex":1219,"latexHtml":1220,"conditionsHtml":895,"figureHtml":1221,"figureCaption":1222,"variables":1223,"summary":1231,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","pythagorean-theorem","Satz des Pythagoras","a^2 + b^2 = c^2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a^2 + b^2 = c^2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" 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mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 273.6 211.2\" width=\"273.6\" height=\"211.2\" role=\"img\" aria-label=\"Rechtwinkliges Dreieck mit den Katheten a und b und der Hypotenuse c\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-pythagorean-theorem-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-pythagorean-theorem-clip\">\u003Crect x=\"0\" y=\"0\" width=\"273.6\" height=\"211.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"43.2,172.8 235.2,172.8 43.2,28.8\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 55.2 172.8 L 55.2 160.8 L 43.2 160.8\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"49.2\" cy=\"166.8\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"139.2\" y=\"192\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"24\" y=\"100.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"153.6\" y=\"84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ccircle cx=\"43.2\" cy=\"172.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"25.200000000000003\" y=\"184.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003Ccircle cx=\"235.2\" cy=\"172.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"241.2\" y=\"184.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"43.2\" cy=\"28.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"25.200000000000003\" y=\"24.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003C\u002Fsvg>","Rechtwinkliges Dreieck mit den Katheten a und b und der Hypotenuse c",[1224,1228,1229],{"symbol":1225,"meaning":1226,"symbolHtml":1227},"a, b","Katheten, die beiden Seiten am rechten Winkel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":964,"meaning":965,"symbolHtml":966},{"symbol":910,"meaning":1230,"symbolHtml":912},"Winkel gegenüber von c (der rechte Winkel)","Im rechtwinkligen Dreieck ist die Summe der Kathetenquadrate gleich dem Hypotenusenquadrat.",{"stem":1233,"formulaId":1234,"title":1235,"latex":1236,"latexHtml":1237,"conditionsHtml":1238,"figureHtml":1239,"figureCaption":1240,"variables":1241,"summary":1252,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-thales","thales-theorem","Satz des Thales","\\gamma = 90^\\circ","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>90\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\gamma = 90^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0556em;\">γ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7241em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">9\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7241em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">liegt auf dem Kreis mit dem Durchmesser\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{AB},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C \\neq A,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" 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Winkel.",{"stem":1254,"formulaId":1255,"title":1256,"latex":1257,"latexHtml":1258,"conditionsHtml":553,"figureHtml":1259,"figureCaption":1260,"variables":1261,"summary":1272,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fschwerpunkt-dreieck","triangle-centroid","Schwerpunkt eines Dreiecks","S\\left(\\frac{x_A + x_B + x_C}{3} \\,\\middle|\\, \\frac{y_A + y_B + y_C}{3}\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmrow>\u003Cmo 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Dreiecks hat als Koordinaten die Mittelwerte der drei Eckpunkt-Koordinaten.",{"stem":1274,"formulaId":1275,"title":1276,"latex":1277,"latexHtml":1278,"conditionsHtml":1279,"figureHtml":1280,"figureCaption":1281,"variables":1282,"summary":1293,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsehnensatz","intersecting-chords","Sehnensatz","\\overline{SA} \\cdot \\overline{SB} = \\overline{SC} \\cdot \\overline{SD}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>D\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{SA} \\cdot \\overline{SB} = \\overline{SC} \\cdot \\overline{SD}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">liegt im Inneren des Kreises\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 254.4 254.4\" width=\"254.4\" height=\"254.4\" role=\"img\" aria-label=\"Zwei Sehnen AB und CD eines Kreises schneiden sich im Punkt S\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-intersecting-chords-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-intersecting-chords-clip\">\u003Crect x=\"0\" y=\"0\" width=\"254.4\" height=\"254.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"127.2\" cy=\"127.2\" r=\"105.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"22.94\" y1=\"144.1\" x2=\"225.94\" y2=\"89.71\" class=\"fig-main\"\u002F>\u003Cline x1=\"116.69\" y1=\"22.13\" x2=\"186.67\" y2=\"214.46\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"22.94\" cy=\"144.1\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"1.9400000000000013\" y=\"146.1\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"225.94\" cy=\"89.71\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"233.94\" y=\"84.71\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"116.69\" cy=\"22.13\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"109.69\" y=\"7.129999999999999\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003Ccircle cx=\"186.67\" cy=\"214.46\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"188.67\" y=\"226.46\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">D\u003C\u002Ftext>\u003Ccircle cx=\"148.8\" cy=\"110.4\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"154.8\" y=\"98.4\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">S\u003C\u002Ftext>\u003C\u002Fsvg>","Zwei Sehnen AB und CD eines Kreises schneiden sich im Punkt S",[1283,1285,1289],{"symbol":946,"meaning":1284,"symbolHtml":948},"Schnittpunkt der beiden Sehnen",{"symbol":1286,"meaning":1287,"symbolHtml":1288},"\\overline{SA}, \\overline{SB}","Längen der beiden Abschnitte der ersten Sehne AB","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{SA}, \\overline{SB}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1290,"meaning":1291,"symbolHtml":1292},"\\overline{SC}, \\overline{SD}","Längen der beiden Abschnitte der zweiten Sehne CD","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>D\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{SC}, \\overline{SD}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Schneiden sich zwei Sehnen eines Kreises, ist das Produkt der Abschnitte bei beiden Sehnen gleich.",{"stem":1295,"formulaId":1296,"title":1297,"latex":1298,"latexHtml":1299,"conditionsHtml":1300,"figureHtml":1301,"figureCaption":1302,"variables":1303,"summary":1314,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsekanten-tangenten-satz","secant-tangent-theorem","Sekanten-Tangenten-Satz","\\overline{PT}^{\\,2} = \\overline{PA} \\cdot \\overline{PB}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmrow>\u003Cmtext> \u003C\u002Fmtext>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overline{PT}^{\\,2} = \\overline{PA} \\cdot \\overline{PB}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0873em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0873em;\">\u003Cspan style=\"top:-3.3362em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mspace mtight\" style=\"margin-right:0.1952em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">liegt außerhalb des Kreises\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 264.5 177.1\" width=\"264.5\" height=\"177.1\" role=\"img\" aria-label=\"Von P aus berührt die Tangente den Kreis in T, die Sekante schneidet ihn in A und B\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-secant-tangent-theorem-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-secant-tangent-theorem-clip\">\u003Crect x=\"0\" y=\"0\" width=\"264.5\" height=\"177.1\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"177.1\" cy=\"89.7\" r=\"69\" class=\"fig-muted\"\u002F>\u003Cline x1=\"177.1\" y1=\"89.7\" x2=\"146.65\" y2=\"27.78\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 135.88 33.07 L 141.18 43.84 L 151.95 38.55\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"143.91\" cy=\"35.81\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Cline x1=\"20.7\" y1=\"89.7\" x2=\"146.65\" y2=\"27.78\" class=\"fig-main\"\u002F>\u003Cline x1=\"20.7\" y1=\"89.7\" x2=\"223.93\" y2=\"140.39\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"20.7\" cy=\"89.7\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"2.6999999999999993\" y=\"93.7\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">P\u003C\u002Ftext>\u003Ccircle cx=\"146.65\" cy=\"27.78\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"142.65\" y=\"13.780000000000001\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">T\u003C\u002Ftext>\u003Ccircle cx=\"111.96\" cy=\"112.47\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"93.96\" y=\"125.47\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"223.93\" cy=\"140.39\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"231.93\" y=\"152.39\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"177.1\" cy=\"89.7\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"183.1\" y=\"79.7\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Von P aus berührt die Tangente den Kreis in T, die Sekante schneidet ihn in A und B",[1304,1308,1312],{"symbol":1305,"meaning":1306,"symbolHtml":1307},"P","Punkt außerhalb des Kreises","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1309,"meaning":1310,"symbolHtml":1311},"T","Berührpunkt einer Tangente von P an den Kreis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">T\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1243,"meaning":1313,"symbolHtml":1245},"die beiden Schnittpunkte einer Sekante durch P mit dem Kreis, A liegt näher an P","Von einem Punkt außerhalb des Kreises ist das Quadrat des Tangentenabschnitts gleich dem Produkt der Sekantenabschnitte.",{"stem":1316,"formulaId":1317,"title":1318,"latex":1319,"latexHtml":1320,"conditionsHtml":1321,"figureHtml":1322,"figureCaption":1323,"variables":1324,"summary":1339,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fstrahlensatz","intercept-theorem","Strahlensatz","\\frac{\\overline{SA_2}}{\\overline{SA_1}} = \\frac{\\overline{SB_2}}{\\overline{SB_1}}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmfrac>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">‾\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{\\overline{SA_2}}{\\overline{SA_1}} = \\frac{\\overline{SB_2}}{\\overline{SB_1}}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4837em;vertical-align:-0.9233em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5603em;\">\u003Cspan style=\"top:-2.2267em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9233em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4837em;vertical-align:-0.9233em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5603em;\">\u003Cspan style=\"top:-2.2267em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-overline\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8833em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8033em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"overline-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan 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style=\"height:0.9233em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∥\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A_1B_1 \\parallel A_2B_2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" 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text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003Ctspan class=\"fig-sub\" dy=\"4\">2\u003C\u002Ftspan>\u003C\u002Ftext>\u003C\u002Fsvg>","Zwei Strahlen mit dem Scheitelpunkt S, geschnitten von den Parallelen A₁B₁ und A₂B₂",[1325,1327,1331,1335],{"symbol":946,"meaning":1326,"symbolHtml":948},"Scheitelpunkt, in dem die beiden Strahlen beginnen",{"symbol":1328,"meaning":1329,"symbolHtml":1330},"A_1, A_2","Schnittpunkte der beiden Parallelen mit dem ersten Strahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A_1, 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style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1332,"meaning":1333,"symbolHtml":1334},"B_1, B_2","Schnittpunkte der beiden Parallelen mit dem zweiten Strahl","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">B_1, B_2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1225,"meaning":1354,"symbolHtml":1227},"die beiden Halbachsen, also halbe Länge und halbe Breite der Ellipse","Für den Umfang einer Ellipse gibt es keine einfache exakte Formel; die Näherung von Ramanujan ist sehr genau.",{"stem":1357,"formulaId":1358,"title":1359,"latex":1360,"latexHtml":1361,"conditionsHtml":553,"figureHtml":1362,"figureCaption":1363,"variables":1364,"summary":1368,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-dreieck","triangle-perimeter","Umfang eines Dreiecks","U = a + b + c","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U = a + b + c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan 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style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 297.6 196.8\" width=\"297.6\" height=\"196.8\" role=\"img\" aria-label=\"Dreieck mit den Seitenlängen a, b und c; der Umfang ist die Länge des ganzen Randes\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-triangle-perimeter-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath 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fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"105.6\" cy=\"28.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"99.6\" y=\"14.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","Dreieck mit den Seitenlängen a, b und c; der Umfang ist die Länge des ganzen Randes",[1365,1367],{"symbol":1350,"meaning":1366,"symbolHtml":1352},"Umfang, die Länge des ganzen Randes",{"symbol":931,"meaning":1212,"symbolHtml":933},"Der Umfang eines Dreiecks ist die Summe seiner drei Seitenlängen.",{"stem":1370,"formulaId":1371,"title":1372,"latex":1373,"latexHtml":1374,"conditionsHtml":553,"figureHtml":1375,"figureCaption":1376,"variables":1377,"summary":1382,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-kreis","circle-circumference","Umfang eines Kreises","U = 2 \\pi r","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U = 2 \\pi r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan 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r=\"105.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"230.4\" y2=\"124.8\" class=\"fig-muted\"\u002F>\u003Ctext x=\"177.6\" y=\"110.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"214.08\" y=\"35.52\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">U\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Kreis mit Mittelpunkt M und Radius r, der Umfang U ist die Länge der Kreislinie",[1378,1380,1381],{"symbol":1350,"meaning":1379,"symbolHtml":1352},"Umfang des Kreises, die Länge der Kreislinie",{"symbol":723,"meaning":724,"symbolHtml":725},{"symbol":646,"meaning":727,"symbolHtml":648},"Der Umfang eines Kreises ist 2 mal π mal Radius, also π mal Durchmesser.",{"stem":1384,"formulaId":1385,"title":1386,"latex":1387,"latexHtml":1388,"conditionsHtml":553,"figureHtml":1389,"figureCaption":1390,"variables":1391,"summary":1396,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-parallelogramm","parallelogram-perimeter","Umfang eines Parallelogramms","u = 2 \\cdot (a + b)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u = 2 \\cdot (a + b)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 297.6 182.4\" width=\"297.6\" height=\"182.4\" role=\"img\" aria-label=\"Parallelogramm mit den Seitenlängen a und b, jede kommt zweimal vor\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-parallelogram-perimeter-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-parallelogram-perimeter-clip\">\u003Crect x=\"0\" y=\"0\" width=\"297.6\" height=\"182.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,148.8 216,148.8 273.6,33.6 81.6,33.6\" class=\"fig-main\"\u002F>\u003Ctext x=\"120\" y=\"165.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"177.6\" y=\"16.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"37.92\" y=\"83.52\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"259.68\" y=\"98.88\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003C\u002Fsvg>","Parallelogramm mit den Seitenlängen a und b, jede kommt zweimal vor",[1392,1394],{"symbol":1120,"meaning":1393,"symbolHtml":1122},"Umfang, die Länge des ganzen Rands",{"symbol":1225,"meaning":1395,"symbolHtml":1227},"die Längen zweier Seiten, die an einer Ecke zusammenstoßen","Der Umfang eines Parallelogramms ist das Doppelte der Summe zweier benachbarter Seiten.",{"stem":1398,"formulaId":1399,"title":1400,"latex":1401,"latexHtml":1402,"conditionsHtml":553,"figureHtml":1403,"figureCaption":1404,"variables":1405,"summary":1408,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-quadrat","square-perimeter","Umfang eines Quadrats","U = 4a","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>4\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U = 4a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 211.2 211.2\" width=\"211.2\" height=\"211.2\" role=\"img\" aria-label=\"Quadrat mit vier gleich langen Seiten a\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-square-perimeter-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-square-perimeter-clip\">\u003Crect x=\"0\" y=\"0\" width=\"211.2\" height=\"211.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"33.6,177.6 177.6,177.6 177.6,33.6 33.6,33.6\" class=\"fig-main\"\u002F>\u003Cpath d=\"M 45.6 177.6 L 45.6 165.6 L 33.6 165.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"39.6\" cy=\"171.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ctext x=\"105.6\" y=\"194.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"105.6\" y=\"16.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"16.8\" y=\"105.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"194.4\" y=\"105.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003C\u002Fsvg>","Quadrat mit vier gleich langen Seiten a",[1406,1407],{"symbol":1350,"meaning":1366,"symbolHtml":1352},{"symbol":582,"meaning":583,"symbolHtml":584},"Der Umfang eines Quadrats ist viermal die Seitenlänge.",{"stem":1410,"formulaId":1411,"title":1412,"latex":1413,"latexHtml":1414,"conditionsHtml":553,"figureHtml":1415,"figureCaption":1416,"variables":1417,"summary":1421,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-rechteck","rectangle-perimeter","Umfang eines Rechtecks","U = 2a + 2b","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U = 2a + 2b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 294.4 202.4\" width=\"294.4\" height=\"202.4\" role=\"img\" aria-label=\"Rechteck mit zwei Seiten der Länge a und zwei Seiten der Länge b\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-rectangle-perimeter-arrow\" viewBox=\"0 0 10 10\" 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Schenkel, die die Grundseiten verbinden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b, d\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Der Umfang eines Trapezes ist die Summe seiner vier Seitenlängen.",{"stem":1440,"formulaId":1441,"title":1442,"latex":1443,"latexHtml":1444,"conditionsHtml":1445,"figureHtml":1446,"figureCaption":1447,"variables":1448,"summary":1455,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfangswinkelsatz","inscribed-angle-theorem","Umfangswinkelsatz","\\alpha = \\frac{\\mu}{2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>μ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha = \\frac{\\mu}{2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">Scheitel von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">auf dem Kreisbogen, der\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">gegenüberliegt\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 249.6 249.6\" width=\"249.6\" height=\"249.6\" role=\"img\" aria-label=\"Umfangswinkel α und Mittelpunktswinkel μ über derselben Sehne\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-inscribed-angle-theorem-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-inscribed-angle-theorem-clip\">\u003Crect x=\"0\" y=\"0\" width=\"249.6\" height=\"249.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"105.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"38.3\" y1=\"185.38\" x2=\"211.3\" y2=\"185.38\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 124.8 124.8 L 106.78 137.42 A 22 22 0 0 0 142.82 137.42 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"124.8\" y=\"158.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">μ\u003C\u002Ftext>\u003Cpath d=\"M 97.49 22.8 L 89.96 43.47 A 22 22 0 0 0 110.11 40.82 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"101.92\" y=\"56.51\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"38.3\" y2=\"185.38\" class=\"fig-main\"\u002F>\u003Cline x1=\"124.8\" y1=\"124.8\" x2=\"211.3\" y2=\"185.38\" class=\"fig-main\"\u002F>\u003Cline x1=\"97.49\" y1=\"22.8\" x2=\"38.3\" y2=\"185.38\" class=\"fig-main\"\u002F>\u003Cline x1=\"97.49\" y1=\"22.8\" x2=\"211.3\" y2=\"185.38\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"38.3\" cy=\"185.38\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"211.3\" cy=\"185.38\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"97.49\" cy=\"22.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"110.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","Umfangswinkel α und Mittelpunktswinkel μ über derselben Sehne",[1449,1451],{"symbol":766,"meaning":1450,"symbolHtml":768},"Umfangswinkel, sein Scheitel liegt auf dem Kreis, seine Schenkel gehen durch die Enden der Sehne",{"symbol":1452,"meaning":1453,"symbolHtml":1454},"\\mu","Mittelpunktswinkel, sein Scheitel liegt im Kreismittelpunkt, er steht über demselben Bogen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Jeder Umfangswinkel über einem Kreisbogen ist halb so groß wie der Mittelpunktswinkel über diesem Bogen.",{"stem":1457,"formulaId":1458,"title":1459,"latex":1460,"latexHtml":1461,"conditionsHtml":1462,"figureHtml":1463,"figureCaption":1464,"variables":1465,"summary":1472,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumkreisradius","circumcircle-radius","Umkreisradius eines Dreiecks","R = \\frac{a}{2 \\sin \\alpha} = \\frac{a \\cdot b \\cdot c}{4A}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmn>4\u003C\u002Fmn>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R = \\frac{a}{2 \\sin \\alpha} = \\frac{a \\cdot b \\cdot c}{4A}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmn>0\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003Cmo><\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0^\\circ < \\alpha < 180^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7132em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6741em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">18\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6741em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 240 240\" width=\"240\" height=\"240\" role=\"img\" aria-label=\"Dreieck mit den Seiten a, b, c und dem Winkel α, dazu der Umkreis mit dem Mittelpunkt M und dem Radius R\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-circumcircle-radius-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-circumcircle-radius-clip\">\u003Crect x=\"0\" y=\"0\" width=\"240\" height=\"240\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Ccircle cx=\"120\" cy=\"120\" r=\"96\" class=\"fig-main\"\u002F>\u003Cpolygon points=\"36.86,168 203.14,168 103.34,25.44\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"120\" y1=\"120\" x2=\"203.14\" y2=\"168\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 36.86 168 L 58.86 168 A 22 22 0 0 0 46.16 148.06 Z\" class=\"fig-angle\"\u002F>\u003Ctext x=\"65.54\" y=\"149.73\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">α\u003C\u002Ftext>\u003Ccircle cx=\"120\" cy=\"120\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"112\" y=\"108\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003Ctext x=\"149.76\" y=\"123.84\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">R\u003C\u002Ftext>\u003Ctext x=\"167.04\" y=\"86.88\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"57.12\" y=\"90.72\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"120\" y=\"183.36\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003Ccircle cx=\"36.86\" cy=\"168\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"18.86\" y=\"176\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">A\u003C\u002Ftext>\u003Ccircle cx=\"203.14\" cy=\"168\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"211.14\" y=\"176\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">B\u003C\u002Ftext>\u003Ccircle cx=\"103.34\" cy=\"25.44\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"99.34\" y=\"11.440000000000001\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">C\u003C\u002Ftext>\u003C\u002Fsvg>","Dreieck mit den Seiten a, b, c und dem Winkel α, dazu der Umkreis mit dem Mittelpunkt M und dem Radius R",[1466,1468,1469,1471],{"symbol":1093,"meaning":1467,"symbolHtml":1095},"Radius des Umkreises",{"symbol":931,"meaning":932,"symbolHtml":933},{"symbol":766,"meaning":1470,"symbolHtml":768},"Winkel gegenüber der Seite a",{"symbol":638,"meaning":707,"symbolHtml":640},"Der Umkreisradius folgt aus einer Seite und dem gegenüberliegenden Winkel oder aus allen drei Seiten und der Fläche.",{"stem":1474,"formulaId":1475,"title":1476,"latex":1477,"latexHtml":1478,"conditionsHtml":553,"figureHtml":1479,"figureCaption":1480,"variables":1481,"summary":1487,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kugel","sphere-volume","Volumen einer Kugel","V = \\frac{4}{3} \\pi r^3","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>4\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{4}{3} \\pi r^3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 235.2 235.2\" width=\"235.2\" height=\"235.2\" role=\"img\" aria-label=\"Kugel mit dem Mittelpunkt M und dem Radius r\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-sphere-volume-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-sphere-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"235.2\" height=\"235.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cellipse cx=\"117.6\" cy=\"117.6\" rx=\"96\" ry=\"96\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 213.6 117.6 A 96 28.8 0 0 0 21.6 117.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 21.6 117.6 A 96 28.8 0 0 0 213.6 117.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"117.6\" y1=\"117.6\" x2=\"213.6\" y2=\"117.6\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"117.6\" cy=\"117.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"111.6\" y=\"133.6\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003Ctext x=\"165.6\" y=\"107.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"79.2\" y=\"60\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">V\u003C\u002Ftext>\u003C\u002Fsvg>","Kugel mit dem Mittelpunkt M und dem Radius r",[1482,1484,1486],{"symbol":1001,"meaning":1483,"symbolHtml":1003},"Volumen der Kugel",{"symbol":723,"meaning":1485,"symbolHtml":725},"Radius der Kugel, der Abstand vom Mittelpunkt zur Oberfläche",{"symbol":646,"meaning":727,"symbolHtml":648},"Das Volumen einer Kugel ist vier Drittel mal π mal Radius hoch 3.",{"stem":1489,"formulaId":1490,"title":1491,"latex":1492,"latexHtml":1493,"conditionsHtml":553,"figureHtml":1494,"figureCaption":1495,"variables":1496,"summary":1502,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-pyramide","pyramid-volume","Volumen einer Pyramide","V = \\frac{1}{3} \\cdot G \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{1}{3} \\cdot G \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 254.4 220.8\" width=\"254.4\" height=\"220.8\" role=\"img\" aria-label=\"Pyramide mit quadratischer Grundfläche G und der Höhe h von der Spitze senkrecht auf die Grundfläche\" 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display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>h\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>R\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\pi h \\left(R^2 - r^2\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan 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r und Höhe h; nur der Ring zwischen den Zylindern zählt",[1512,1514,1516,1518],{"symbol":1001,"meaning":1513,"symbolHtml":1003},"Volumen des Materials (ohne den Hohlraum)",{"symbol":1093,"meaning":1515,"symbolHtml":1095},"Außenradius",{"symbol":723,"meaning":1517,"symbolHtml":725},"Innenradius",{"symbol":693,"meaning":1519,"symbolHtml":695},"Höhe bzw. Länge des Zylinders","Das Volumen eines Hohlzylinders ist das Volumen des äußeren Zylinders minus das des inneren Hohlraums.",{"stem":1522,"formulaId":1523,"title":1524,"latex":1525,"latexHtml":1526,"conditionsHtml":553,"figureHtml":1527,"figureCaption":1528,"variables":1529,"summary":1536,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegel","cone-volume","Volumen eines Kegels","V = \\frac{1}{3} \\pi r^2 h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V 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Kegels, der senkrechte Abstand der Spitze von der Grundfläche",{"symbol":646,"meaning":727,"symbolHtml":648},"Das Volumen eines Kegels ist ein Drittel des Zylinders mit gleicher Grundfläche und Höhe.",{"stem":1538,"formulaId":1539,"title":1540,"latex":1541,"latexHtml":1542,"conditionsHtml":1543,"figureHtml":1544,"figureCaption":1545,"variables":1546,"summary":1556,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf","frustum-volume","Volumen eines Kegelstumpfs","V = \\frac{\\pi h}{3} \\left(R^2 + R r + r^2\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>R\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>R\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{\\pi h}{3} \\left(R^2 + R r + r^2\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R \\geq r \\geq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 230.4 182.4\" width=\"230.4\" height=\"182.4\" role=\"img\" aria-label=\"Kegelstumpf mit dem Radius R der Grundfläche, dem Radius r der Deckfläche und der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-frustum-volume-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-frustum-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"230.4\" height=\"182.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,141.6 25.3,146.11 29.23,150.48 35.57,154.56 44.21,158.26 54.86,161.47 67.2,164.06 80.83,165.94 95.38,167.14 110.4,167.52 125.42,167.14 139.97,165.94 153.6,164.06 165.94,161.47 176.59,158.26 185.23,154.56 191.57,150.48 195.5,146.11 196.8,141.6 158.4,36 156.77,32.26 151.97,28.8 144.34,25.82 134.4,23.52 122.83,22.08 110.4,21.6 97.97,22.08 86.4,23.52 76.46,25.82 68.83,28.8 64.03,32.26 62.4,36\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 196.8 141.6 A 86.4 25.92 0 0 0 24 141.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24 141.6 A 86.4 25.92 0 0 0 196.8 141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"24\" y1=\"141.6\" x2=\"62.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"196.8\" y1=\"141.6\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cellipse cx=\"110.4\" cy=\"36\" rx=\"48\" ry=\"14.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"196.8\" y2=\"141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"36\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"110.4\" y2=\"36\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 110.4 129.6 L 122.4 129.6 L 122.4 141.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"116.4\" cy=\"135.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"141.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"36\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"153.6\" y=\"153.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">R\u003C\u002Ftext>\u003Ctext x=\"172.8\" y=\"24\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"98.4\" y=\"88.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","Kegelstumpf mit dem Radius R der Grundfläche, dem Radius r der Deckfläche und der Höhe h",[1547,1549,1551,1553,1555],{"symbol":1001,"meaning":1548,"symbolHtml":1003},"Volumen des Kegelstumpfs",{"symbol":693,"meaning":1550,"symbolHtml":695},"Höhe, der senkrechte Abstand von Grund- und Deckfläche",{"symbol":1093,"meaning":1552,"symbolHtml":1095},"Radius der größeren Kreisfläche",{"symbol":723,"meaning":1554,"symbolHtml":725},"Radius der kleineren Kreisfläche",{"symbol":646,"meaning":647,"symbolHtml":648},"Ein Kegelstumpf mit den Radien R und r und der Höhe h hat das Volumen πh\u002F3 · (R² + Rr + r²).",{"stem":1558,"formulaId":1559,"title":1560,"latex":1561,"latexHtml":1562,"conditionsHtml":553,"figureHtml":1563,"figureCaption":1564,"variables":1565,"summary":1571,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-prisma","prism-volume","Volumen eines Prismas","V = G \\cdot h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = G \\cdot h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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Dreiecksprisma mit der Grundfläche G und der Höhe h",[1566,1568,1569],{"symbol":1001,"meaning":1567,"symbolHtml":1003},"Volumen des Prismas",{"symbol":1116,"meaning":1117,"symbolHtml":1118},{"symbol":693,"meaning":1570,"symbolHtml":695},"Höhe des Prismas, der senkrechte Abstand zwischen Grund- und Deckfläche","Das Volumen eines Prismas ist Grundfläche mal Höhe.",{"stem":1573,"formulaId":1574,"title":1575,"latex":1576,"latexHtml":1577,"conditionsHtml":1578,"figureHtml":1579,"figureCaption":1580,"variables":1581,"summary":1590,"level":650,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-pyramidenstumpf","pyramid-frustum-volume","Volumen eines Pyramidenstumpfs","V = \\frac{h}{3} \\left(G + \\sqrt{G \\cdot D} + D\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>h\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>D\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>D\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{h}{3} \\left(G + \\sqrt{G \\cdot D} + D\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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class=\"fig-dot\"\u002F>\u003Ccircle cx=\"129.6\" cy=\"137.28\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"129.6\" cy=\"36.48\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"117.6\" y=\"93.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003Ctext x=\"88.8\" y=\"140.64\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">G\u003C\u002Ftext>\u003Ctext x=\"151.2\" y=\"35.52\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">D\u003C\u002Ftext>\u003C\u002Fsvg>","Pyramidenstumpf mit Grundfläche G, paralleler Deckfläche D und der Höhe h",[1582,1584,1585,1586],{"symbol":1001,"meaning":1583,"symbolHtml":1003},"Volumen des Pyramidenstumpfs",{"symbol":693,"meaning":1550,"symbolHtml":695},{"symbol":1116,"meaning":1117,"symbolHtml":1118},{"symbol":1587,"meaning":1588,"symbolHtml":1589},"D","Flächeninhalt der Deckfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>D\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">D\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Das Volumen eines Pyramidenstumpfs folgt aus Höhe, Grundfläche G und Deckfläche D.",{"stem":1592,"formulaId":1593,"title":1594,"latex":1595,"latexHtml":1596,"conditionsHtml":553,"figureHtml":1597,"figureCaption":1598,"variables":1599,"summary":1605,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-quader","cuboid-volume","Volumen eines Quaders","V = a \\cdot b \\cdot c","\u003Cspan 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Höhe.",{"stem":1607,"formulaId":1608,"title":1609,"latex":1610,"latexHtml":1611,"conditionsHtml":553,"figureHtml":1612,"figureCaption":1613,"variables":1614,"summary":1617,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-wuerfel","cube-volume","Volumen eines Würfels","V = a^3","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = a^3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan 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3.",{"stem":1619,"formulaId":1620,"title":1621,"latex":1622,"latexHtml":1623,"conditionsHtml":553,"figureHtml":1624,"figureCaption":1625,"variables":1626,"summary":1632,"level":586,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-zylinder","cylinder-volume","Volumen eines Zylinders","V = \\pi r^2 h","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\pi r^2 h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8641em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 206.4 194.4\" width=\"206.4\" height=\"194.4\" role=\"img\" aria-label=\"Zylinder mit dem Radius r der Grundfläche und der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cylinder-volume-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-cylinder-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"206.4\" height=\"194.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,158.4 25.1,162.14 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class=\"fig-dot\"\u002F>\u003Ctext x=\"132\" y=\"23.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"182.4\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","Zylinder mit dem Radius r der Grundfläche und der Höhe h",[1627,1629,1630,1631],{"symbol":1001,"meaning":1628,"symbolHtml":1003},"Volumen des Zylinders",{"symbol":723,"meaning":1075,"symbolHtml":725},{"symbol":693,"meaning":1170,"symbolHtml":695},{"symbol":646,"meaning":727,"symbolHtml":648},"Das Volumen eines Zylinders ist Kreisfläche mal Höhe, also π mal r² mal h.",{"stem":1634,"formulaId":1635,"title":1636,"latex":1637,"latexHtml":1638,"conditionsHtml":553,"figureHtml":1639,"figureCaption":1640,"variables":1641,"summary":1646,"level":566,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fwinkelsumme-dreieck","triangle-angle-sum","Winkelsumme im Dreieck","\\alpha + \\beta + \\gamma = 180^\\circ","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>β\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>γ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha + \\beta + \\gamma = 180^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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