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\\approx \\pi \\left(3 \\cdot 8 - \\sqrt{18 \\cdot 14}\\right) = \\pi \\left(24 - \\sqrt{252}\\right) \\approx 25{,}53\\,\\text{cm}",[567,1073,1075,1094,1248,1343],{"className":1074,"ariaHidden":611},[610],[567,1076,1078,1081,1085,1088,1091],{"className":1077},[615],[567,1079],{"className":1080,"style":620},[619],[567,1082,1002],{"className":1083,"style":1084},[624,625],"margin-right:0.109em;",[567,1086],{"className":1087,"style":630},[629],[567,1089,1005],{"className":1090},[634],[567,1092],{"className":1093,"style":630},[629],[567,1095,1097,1101,1104,1107,1239,1242,1245],{"className":1096},[615],[567,1098],{"className":1099,"style":1100},[619],"height:1.8em;vertical-align:-0.65em;",[567,1102,595],{"className":1103,"style":648},[624,625],[567,1105],{"className":1106,"style":908},[629],[567,1108,1111,1122,1125,1129,1133,1136,1139,1142,1145,1148,1232],{"className":1109},[1110],"minner",[567,1112,1117],{"className":1113,"style":1116},[1114,1115],"mopen","delimcenter","top:0em;",[567,1118,1012],{"className":1119},[1120,1121],"delimsizing","size2",[567,1123,935],{"className":1124},[624],[567,1126],{"className":1127,"style":1128},[629],"margin-right:0.2222em;",[567,1130,1017],{"className":1131},[1132],"mbin",[567,1134],{"className":1135,"style":1128},[629],[567,1137,1020],{"className":1138},[624],[567,1140],{"className":1141,"style":1128},[629],[567,1143,1023],{"className":1144},[1132],[567,1146],{"className":1147,"style":1128},[629],[567,1149,1152],{"className":1150},[624,1151],"sqrt",[567,1153,1157,1223],{"className":1154},[1155,1156],"vlist-t","vlist-t2",[567,1158,1161,1218],{"className":1159},[1160],"vlist-r",[567,1162,1166,1195],{"className":1163,"style":1165},[1164],"vlist","height:0.9561em;",[567,1167,1171,1176],{"className":1168,"style":1170},[1169],"svg-align","top:-3em;",[567,1172],{"className":1173,"style":1175},[1174],"pstrut","height:3em;",[567,1177,1180,1183,1186,1189,1192],{"className":1178,"style":1179},[624],"padding-left:0.833em;",[567,1181,1031],{"className":1182},[624],[567,1184],{"className":1185,"style":1128},[629],[567,1187,1017],{"className":1188},[1132],[567,1190],{"className":1191,"style":1128},[629],[567,1193,1036],{"className":1194},[624],[567,1196,1198,1201],{"style":1197},"top:-2.9161em;",[567,1199],{"className":1200,"style":1175},[1174],[567,1202,1206],{"className":1203,"style":1205},[1204],"hide-tail","min-width:0.853em;height:1.08em;",[1207,1208,1214],"svg",{"xmlns":1209,"width":1210,"height":1211,"viewBox":1212,"preserveAspectRatio":1213},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1215,1216],"path",{"d":1217},"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",[567,1219,1222],{"className":1220},[1221],"vlist-s","​",[567,1224,1226],{"className":1225},[1160],[567,1227,1230],{"className":1228,"style":1229},[1164],"height:0.0839em;",[567,1231],{},[567,1233,1236],{"className":1234,"style":1116},[1235,1115],"mclose",[567,1237,1039],{"className":1238},[1120,1121],[567,1240],{"className":1241,"style":630},[629],[567,1243,592],{"className":1244},[634],[567,1246],{"className":1247,"style":630},[629],[567,1249,1251,1254,1257,1260,1334,1337,1340],{"className":1250},[615],[567,1252],{"className":1253,"style":1100},[619],[567,1255,595],{"className":1256,"style":648},[624,625],[567,1258],{"className":1259,"style":908},[629],[567,1261,1263,1269,1272,1275,1278,1281,1328],{"className":1262},[1110],[567,1264,1266],{"className":1265,"style":1116},[1114,1115],[567,1267,1012],{"className":1268},[1120,1121],[567,1270,1050],{"className":1271},[624],[567,1273],{"className":1274,"style":1128},[629],[567,1276,1023],{"className":1277},[1132],[567,1279],{"className":1280,"style":1128},[629],[567,1282,1284],{"className":1283},[624,1151],[567,1285,1287,1320],{"className":1286},[1155,1156],[567,1288,1290,1317],{"className":1289},[1160],[567,1291,1293,1305],{"className":1292,"style":1165},[1164],[567,1294,1296,1299],{"className":1295,"style":1170},[1169],[567,1297],{"className":1298,"style":1175},[1174],[567,1300,1302],{"className":1301,"style":1179},[624],[567,1303,1057],{"className":1304},[624],[567,1306,1307,1310],{"style":1197},[567,1308],{"className":1309,"style":1175},[1174],[567,1311,1313],{"className":1312,"style":1205},[1204],[1207,1314,1315],{"xmlns":1209,"width":1210,"height":1211,"viewBox":1212,"preserveAspectRatio":1213},[1215,1316],{"d":1217},[567,1318,1222],{"className":1319},[1221],[567,1321,1323],{"className":1322},[1160],[567,1324,1326],{"className":1325,"style":1229},[1164],[567,1327],{},[567,1329,1331],{"className":1330,"style":1116},[1235,1115],[567,1332,1039],{"className":1333},[1120,1121],[567,1335],{"className":1336,"style":630},[629],[567,1338,1005],{"className":1339},[634],[567,1341],{"className":1342,"style":630},[629],[567,1344,1346,1350,1354,1362,1366,1369],{"className":1345},[615],[567,1347],{"className":1348,"style":1349},[619],"height:0.8389em;vertical-align:-0.1944em;",[567,1351,1353],{"className":1352},[624],"25",[567,1355,1357],{"className":1356},[624],[567,1358,1361],{"className":1359},[1360],"mpunct",",",[567,1363,1365],{"className":1364},[624],"53",[567,1367],{"className":1368,"style":908},[629],[567,1370,1372],{"className":1371},[624,912],[567,1373,871],{"className":1374},[624],[563,1376,1377,1378,1520],{},"Der exakte Umfang stimmt auf die angegebenen Stellen überein. Die grobe Schätzung ",[567,1379,1381,1422],{"className":1380},[570],[567,1382,1384],{"className":1383},[574],[576,1385,1386],{"xmlns":578},[580,1387,1388,1419],{},[583,1389,1390,1392,1395,1397,1400,1402,1404,1406,1408,1410,1412,1415,1417],{},[586,1391,595],{},[590,1393,1012],{"stretchy":1394},"false",[586,1396,598],{},[590,1398,1399],{},"+",[586,1401,601],{},[590,1403,1039],{"stretchy":1394},[590,1405,592],{},[680,1407,1020],{},[586,1409,595],{},[590,1411,1005],{},[680,1413,1414],{},"25,13",[866,1416,868],{},[866,1418,871],{},[603,1420,1421],{"encoding":605},"\\pi(a + b) = 8\\pi \\approx 25{,}13\\,\\text{cm}",[567,1423,1425,1450,1471,1492],{"className":1424,"ariaHidden":611},[610],[567,1426,1428,1432,1435,1438,1441,1444,1447],{"className":1427},[615],[567,1429],{"className":1430,"style":1431},[619],"height:1em;vertical-align:-0.25em;",[567,1433,595],{"className":1434,"style":648},[624,625],[567,1436,1012],{"className":1437},[1114],[567,1439,598],{"className":1440},[624,625],[567,1442],{"className":1443,"style":1128},[629],[567,1445,1399],{"className":1446},[1132],[567,1448],{"className":1449,"style":1128},[629],[567,1451,1453,1456,1459,1462,1465,1468],{"className":1452},[615],[567,1454],{"className":1455,"style":1431},[619],[567,1457,601],{"className":1458},[624,625],[567,1460,1039],{"className":1461},[1235],[567,1463],{"className":1464,"style":630},[629],[567,1466,592],{"className":1467},[634],[567,1469],{"className":1470,"style":630},[629],[567,1472,1474,1477,1480,1483,1486,1489],{"className":1473},[615],[567,1475],{"className":1476,"style":713},[619],[567,1478,1020],{"className":1479},[624],[567,1481,595],{"className":1482,"style":648},[624,625],[567,1484],{"className":1485,"style":630},[629],[567,1487,1005],{"className":1488},[634],[567,1490],{"className":1491,"style":630},[629],[567,1493,1495,1498,1501,1507,1511,1514],{"className":1494},[615],[567,1496],{"className":1497,"style":1349},[619],[567,1499,1353],{"className":1500},[624],[567,1502,1504],{"className":1503},[624],[567,1505,1361],{"className":1506},[1360],[567,1508,1510],{"className":1509},[624],"13",[567,1512],{"className":1513,"style":908},[629],[567,1515,1517],{"className":1516},[624,912],[567,1518,871],{"className":1519},[624]," ist dagegen zu klein.",[558,1522,1524],{"id":1523},"typische-fehler","Typische Fehler",[1526,1527,1528,1589,1629],"ul",{},[1529,1530,1531,1532,916,1560,1588],"li",{},"Ganze Achsen statt Halbachsen einsetzen. ",[567,1533,1535,1548],{"className":1534},[570],[567,1536,1538],{"className":1537},[574],[576,1539,1540],{"xmlns":578},[580,1541,1542,1546],{},[583,1543,1544],{},[586,1545,598],{},[603,1547,598],{"encoding":605},[567,1549,1551],{"className":1550,"ariaHidden":611},[610],[567,1552,1554,1557],{"className":1553},[615],[567,1555],{"className":1556,"style":756},[619],[567,1558,598],{"className":1559},[624,625],[567,1561,1563,1576],{"className":1562},[570],[567,1564,1566],{"className":1565},[574],[576,1567,1568],{"xmlns":578},[580,1569,1570,1574],{},[583,1571,1572],{},[586,1573,601],{},[603,1575,601],{"encoding":605},[567,1577,1579],{"className":1578,"ariaHidden":611},[610],[567,1580,1582,1585],{"className":1581},[615],[567,1583],{"className":1584,"style":644},[619],[567,1586,601],{"className":1587},[624,625]," sind die Abstände vom Mittelpunkt zum Rand.",[1529,1590,1591,1592,1628],{},"Die Flächenformel ",[567,1593,1595,1613],{"className":1594},[570],[567,1596,1598],{"className":1597},[574],[576,1599,1600],{"xmlns":578},[580,1601,1602,1610],{},[583,1603,1604,1606,1608],{},[586,1605,595],{},[586,1607,598],{},[586,1609,601],{},[603,1611,1612],{"encoding":605},"\\pi a b",[567,1614,1616],{"className":1615,"ariaHidden":611},[610],[567,1617,1619,1622,1625],{"className":1618},[615],[567,1620],{"className":1621,"style":644},[619],[567,1623,595],{"className":1624,"style":648},[624,625],[567,1626,652],{"className":1627},[624,625]," für den Umfang halten.",[1529,1630,1631,1697],{},[567,1632,1634,1658],{"className":1633},[570],[567,1635,1637],{"className":1636},[574],[576,1638,1639],{"xmlns":578},[580,1640,1641,1655],{},[583,1642,1643,1645,1647,1649,1651,1653],{},[586,1644,595],{},[590,1646,1012],{"stretchy":1394},[586,1648,598],{},[590,1650,1399],{},[586,1652,601],{},[590,1654,1039],{"stretchy":1394},[603,1656,1657],{"encoding":605},"\\pi(a + b)",[567,1659,1661,1685],{"className":1660,"ariaHidden":611},[610],[567,1662,1664,1667,1670,1673,1676,1679,1682],{"className":1663},[615],[567,1665],{"className":1666,"style":1431},[619],[567,1668,595],{"className":1669,"style":648},[624,625],[567,1671,1012],{"className":1672},[1114],[567,1674,598],{"className":1675},[624,625],[567,1677],{"className":1678,"style":1128},[629],[567,1680,1399],{"className":1681},[1132],[567,1683],{"className":1684,"style":1128},[629],[567,1686,1688,1691,1694],{"className":1687},[615],[567,1689],{"className":1690,"style":1431},[619],[567,1692,601],{"className":1693},[624,625],[567,1695,1039],{"className":1696},[1235]," als genauen Wert ansehen. Diese Schätzung ist immer zu klein, außer beim Kreis.",{"title":1699,"searchDepth":1700,"depth":1700,"links":1701},"",2,[1702,1703,1704],{"id":560,"depth":1700,"text":561},{"id":841,"depth":1700,"text":842},{"id":1523,"depth":1700,"text":1524},[1706,1709,1712,1714,1716],{"lhs":1707,"rhs":1708},"pi*(3*(a + a) - sqrt((3*a + a)*(a + 3*a)))","2*pi*a",{"lhs":1710,"rhs":1711},"round(pi*(3*(5 + 3) - sqrt((3*5 + 3)*(5 + 3*3))), 2)","25.53",{"lhs":1713,"rhs":1057},"(3*5 + 3)*(5 + 3*3)",{"lhs":1715,"rhs":1711},"round(4*5*sum(map(0:999, f(k) = sqrt(1 - 0.64*sin((k + 0.5)\u002F1000*pi\u002F2)^2)))*(pi\u002F2)\u002F1000, 2)",{"lhs":1717,"rhs":1718},"round(pi*(5 + 3), 2)","25.13","a > 0,\\ b > 0","\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 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