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Einsetzen in ",[574,1198,1200,1248],{"className":1199},[577],[574,1201,1203],{"className":1202},[581],[583,1204,1205],{"xmlns":585},[587,1206,1207,1245],{},[590,1208,1209,1222,1224,1230,1232],{},[593,1210,1211,1213],{},[596,1212,598],{},[590,1214,1215,1217,1220],{},[596,1216,1012],{},[604,1218,1219],{},"+",[600,1221,728],{},[604,1223,606],{},[593,1225,1226,1228],{},[596,1227,598],{},[596,1229,1012],{},[604,1231,1219],{},[593,1233,1234,1236],{},[596,1235,598],{},[590,1237,1238,1240,1243],{},[596,1239,1012],{},[604,1241,1242],{},"−",[600,1244,728],{},[610,1246,1247],{"encoding":612},"F_{n+1} = F_n + 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erfüllt die Rekursion. Die Startwerte 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und 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legen ",[574,2394,2396,2424],{"className":2395},[577],[574,2397,2399],{"className":2398},[581],[583,2400,2401],{"xmlns":585},[587,2402,2403,2421],{},[590,2404,2405,2411,2413],{},[593,2406,2407,2409],{},[596,2408,2019],{},[600,2410,728],{},[604,2412,606],{},[1564,2414,2415,2417],{},[600,2416,728],{},[1573,2418,2419],{},[600,2420,841],{},[610,2422,2423],{"encoding":612},"c_1 = \\frac{1}{\\sqrt{5}}",[574,2425,2427,2483],{"className":2426,"ariaHidden":618},[617],[574,2428,2430,2434,2474,2477,2480],{"className":2429},[622],[574,2431],{"className":2432,"style":2433},[626],"height:0.5806em;vertical-align:-0.15em;",[574,2435,2437,2440],{"className":2436},[631],[574,2438,2019],{"className":2439},[631,635],[574,2441,2443],{"className":2442},[640],[574,2444,2446,2466],{"className":2445},[644,645],[574,2447,2449,2463],{"className":2448},[649],[574,2450,2452],{"className":2451,"style":654},[653],[574,2453,2454,2457],{"style":2074},[574,2455],{"className":2456,"style":662},[661],[574,2458,2460],{"className":2459},[666,667,668,669],[574,2461,728],{"className":2462},[631,669],[574,2464,677],{"className":2465},[676],[574,2467,2469],{"className":2468},[649],[574,2470,2472],{"className":2471,"style":684},[653],[574,2473],{},[574,2475],{"className":2476,"style":691},[690],[574,2478,606],{"className":2479},[695],[574,2481],{"className":2482,"style":691},[690],[574,2484,2486,2490],{"className":2485},[622],[574,2487],{"className":2488,"style":2489},[626],"height:1.3831em;vertical-align:-0.538em;",[574,2491,2493,2496,2606],{"className":2492},[631],[574,2494],{"className":2495},[1654,1655],[574,2497,2499],{"className":2498},[1564],[574,2500,2502,2597],{"className":2501},[644,645],[574,2503,2505,2594],{"className":2504},[649],[574,2506,2509,2571,2579],{"className":2507,"style":2508},[653],"height:0.8451em;",[574,2510,2512,2515],{"style":2511},"top:-2.551em;",[574,2513],{"className":2514,"style":1675},[661],[574,2516,2518],{"className":2517},[666,667,668,669],[574,2519,2521],{"className":2520},[631,669],[574,2522,2524],{"className":2523},[631,1717,669],[574,2525,2527,2562],{"className":2526},[644,645],[574,2528,2530,2559],{"className":2529},[649],[574,2531,2534,2546],{"className":2532,"style":2533},[653],"height:0.9128em;",[574,2535,2537,2540],{"className":2536,"style":1732},[1731],[574,2538],{"className":2539,"style":1675},[661],[574,2541,2543],{"className":2542,"style":1739},[631,669],[574,2544,841],{"className":2545},[631,669],[574,2547,2549,2552],{"style":2548},"top:-2.8728em;",[574,2550],{"className":2551,"style":1675},[661],[574,2553,2555],{"className":2554,"style":1753},[1752,669],[1755,2556,2557],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,2558],{"d":1765},[574,2560,677],{"className":2561},[676],[574,2563,2565],{"className":2564},[649],[574,2566,2569],{"className":2567,"style":2568},[653],"height:0.1272em;",[574,2570],{},[574,2572,2573,2576],{"style":1684},[574,2574],{"className":2575,"style":1675},[661],[574,2577],{"className":2578,"style":1692},[1691],[574,2580,2582,2585],{"style":2581},"top:-3.394em;",[574,2583],{"className":2584,"style":1675},[661],[574,2586,2588],{"className":2587},[666,667,668,669],[574,2589,2591],{"className":2590},[631,669],[574,2592,728],{"className":2593},[631,669],[574,2595,677],{"className":2596},[676],[574,2598,2600],{"className":2599},[649],[574,2601,2604],{"className":2602,"style":2603},[653],"height:0.538em;",[574,2605],{},[574,2607],{"className":2608},[1793,1655],[574,2610,2612,2642],{"className":2611},[577],[574,2613,2615],{"className":2614},[581],[583,2616,2617],{"xmlns":585},[587,2618,2619,2639],{},[590,2620,2621,2627,2629,2631],{},[593,2622,2623,2625],{},[596,2624,2019],{},[600,2626,831],{},[604,2628,606],{},[604,2630,1242],{},[1564,2632,2633,2635],{},[600,2634,728],{},[1573,2636,2637],{},[600,2638,841],{},[610,2640,2641],{"encoding":612},"c_2 = -\\frac{1}{\\sqrt{5}}",[574,2643,2645,2700],{"className":2644,"ariaHidden":618},[617],[574,2646,2648,2651,2691,2694,2697],{"className":2647},[622],[574,2649],{"className":2650,"style":2433},[626],[574,2652,2654,2657],{"className":2653},[631],[574,2655,2019],{"className":2656},[631,635],[574,2658,2660],{"className":2659},[640],[574,2661,2663,2683],{"className":2662},[644,645],[574,2664,2666,2680],{"className":2665},[649],[574,2667,2669],{"className":2668,"style":654},[653],[574,2670,2671,2674],{"style":2074},[574,2672],{"className":2673,"style":662},[661],[574,2675,2677],{"className":2676},[666,667,668,669],[574,2678,831],{"className":2679},[631,669],[574,2681,677],{"className":2682},[676],[574,2684,2686],{"className":2685},[649],[574,2687,2689],{"className":2688,"style":684},[653],[574,2690],{},[574,2692],{"className":2693,"style":691},[690],[574,2695,606],{"className":2696},[695],[574,2698],{"className":2699,"style":691},[690],[574,2701,2703,2706,2709],{"className":2702},[622],[574,2704],{"className":2705,"style":2489},[626],[574,2707,1242],{"className":2708},[631],[574,2710,2712,2715,2818],{"className":2711},[631],[574,2713],{"className":2714},[1654,1655],[574,2716,2718],{"className":2717},[1564],[574,2719,2721,2810],{"className":2720},[644,645],[574,2722,2724,2807],{"className":2723},[649],[574,2725,2727,2785,2793],{"className":2726,"style":2508},[653],[574,2728,2729,2732],{"style":2511},[574,2730],{"className":2731,"style":1675},[661],[574,2733,2735],{"className":2734},[666,667,668,669],[574,2736,2738],{"className":2737},[631,669],[574,2739,2741],{"className":2740},[631,1717,669],[574,2742,2744,2777],{"className":2743},[644,645],[574,2745,2747,2774],{"className":2746},[649],[574,2748,2750,2762],{"className":2749,"style":2533},[653],[574,2751,2753,2756],{"className":2752,"style":1732},[1731],[574,2754],{"className":2755,"style":1675},[661],[574,2757,2759],{"className":2758,"style":1739},[631,669],[574,2760,841],{"className":2761},[631,669],[574,2763,2764,2767],{"style":2548},[574,2765],{"className":2766,"style":1675},[661],[574,2768,2770],{"className":2769,"style":1753},[1752,669],[1755,2771,2772],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,2773],{"d":1765},[574,2775,677],{"className":2776},[676],[574,2778,2780],{"className":2779},[649],[574,2781,2783],{"className":2782,"style":2568},[653],[574,2784],{},[574,2786,2787,2790],{"style":1684},[574,2788],{"className":2789,"style":1675},[661],[574,2791],{"className":2792,"style":1692},[1691],[574,2794,2795,2798],{"style":2581},[574,2796],{"className":2797,"style":1675},[661],[574,2799,2801],{"className":2800},[666,667,668,669],[574,2802,2804],{"className":2803},[631,669],[574,2805,728],{"className":2806},[631,669],[574,2808,677],{"className":2809},[676],[574,2811,2813],{"className":2812},[649],[574,2814,2816],{"className":2815,"style":2603},[653],[574,2817],{},[574,2819],{"className":2820},[1793,1655]," fest. Die Formel lässt sich auch mit vollständiger Induktion beweisen.",[565,2823,2824],{},"Folgerungen:",[2826,2827,2828,3203],"ul",{},[2829,2830,2831,2832,2896,2897,2950,2951,3020,3021,3202],"li",{},"Wegen ",[574,2833,2835,2859],{"className":2834},[577],[574,2836,2838],{"className":2837},[581],[583,2839,2840],{"xmlns":585},[587,2841,2842,2856],{},[590,2843,2844,2847,2849,2851,2854],{},[596,2845,2846],{"mathvariant":1559},"∣",[596,2848,1592],{},[596,2850,2846],{"mathvariant":1559},[604,2852,2853],{},"\u003C",[600,2855,728],{},[610,2857,2858],{"encoding":612},"|\\psi| \u003C 1",[574,2860,2862,2887],{"className":2861,"ariaHidden":618},[617],[574,2863,2865,2869,2872,2875,2878,2881,2884],{"className":2864},[622],[574,2866],{"className":2867,"style":2868},[626],"height:1em;vertical-align:-0.25em;",[574,2870,2846],{"className":2871},[631],[574,2873,1592],{"className":2874,"style":1836},[631,635],[574,2876,2846],{"className":2877},[631],[574,2879],{"className":2880,"style":691},[690],[574,2882,2853],{"className":2883},[695],[574,2885],{"className":2886,"style":691},[690],[574,2888,2890,2893],{"className":2889},[622],[574,2891],{"className":2892,"style":705},[626],[574,2894,728],{"className":2895},[631]," wird der zweite Summand schnell winzig. Für alle ",[574,2898,2900,2919],{"className":2899},[577],[574,2901,2903],{"className":2902},[581],[583,2904,2905],{"xmlns":585},[587,2906,2907,2916],{},[590,2908,2909,2911,2914],{},[596,2910,1012],{},[604,2912,2913],{},"≥",[600,2915,602],{},[610,2917,2918],{"encoding":612},"n \\geq 0",[574,2920,2922,2941],{"className":2921,"ariaHidden":618},[617],[574,2923,2925,2929,2932,2935,2938],{"className":2924},[622],[574,2926],{"className":2927,"style":2928},[626],"height:0.7719em;vertical-align:-0.136em;",[574,2930,1012],{"className":2931},[631,635],[574,2933],{"className":2934,"style":691},[690],[574,2936,2913],{"className":2937},[695],[574,2939],{"className":2940,"style":691},[690],[574,2942,2944,2947],{"className":2943},[622],[574,2945],{"className":2946,"style":705},[626],[574,2948,602],{"className":2949},[631]," ist ",[574,2952,2954,2971],{"className":2953},[577],[574,2955,2957],{"className":2956},[581],[583,2958,2959],{"xmlns":585},[587,2960,2961,2969],{},[590,2962,2963],{},[593,2964,2965,2967],{},[596,2966,598],{},[596,2968,1012],{},[610,2970,1015],{"encoding":612},[574,2972,2974],{"className":2973,"ariaHidden":618},[617],[574,2975,2977,2980],{"className":2976},[622],[574,2978],{"className":2979,"style":627},[626],[574,2981,2983,2986],{"className":2982},[631],[574,2984,598],{"className":2985,"style":636},[631,635],[574,2987,2989],{"className":2988},[640],[574,2990,2992,3012],{"className":2991},[644,645],[574,2993,2995,3009],{"className":2994},[649],[574,2996,2998],{"className":2997,"style":1043},[653],[574,2999,3000,3003],{"style":657},[574,3001],{"className":3002,"style":662},[661],[574,3004,3006],{"className":3005},[666,667,668,669],[574,3007,1012],{"className":3008},[631,635,669],[574,3010,677],{"className":3011},[676],[574,3013,3015],{"className":3014},[649],[574,3016,3018],{"className":3017,"style":684},[653],[574,3019],{}," die nächste ganze Zahl an ",[574,3022,3024,3048],{"className":3023},[577],[574,3025,3027],{"className":3026},[581],[583,3028,3029],{"xmlns":585},[587,3030,3031,3045],{},[590,3032,3033],{},[1564,3034,3035,3041],{},[1091,3036,3037,3039],{},[596,3038,1560],{"mathvariant":1559},[596,3040,1012],{},[1573,3042,3043],{},[600,3044,841],{},[610,3046,3047],{"encoding":612},"\\frac{\\Phi^n}{\\sqrt{5}}",[574,3049,3051],{"className":3050,"ariaHidden":618},[617],[574,3052,3054,3058],{"className":3053},[622],[574,3055],{"className":3056,"style":3057},[626],"height:1.449em;vertical-align:-0.538em;",[574,3059,3061,3064,3199],{"className":3060},[631],[574,3062],{"className":3063},[1654,1655],[574,3065,3067],{"className":3066},[1564],[574,3068,3070,3191],{"className":3069},[644,645],[574,3071,3073,3188],{"className":3072},[649],[574,3074,3077,3135,3143],{"className":3075,"style":3076},[653],"height:0.911em;",[574,3078,3079,3082],{"style":2511},[574,3080],{"className":3081,"style":1675},[661],[574,3083,3085],{"className":3084},[666,667,668,669],[574,3086,3088],{"className":3087},[631,669],[574,3089,3091],{"className":3090},[631,1717,669],[574,3092,3094,3127],{"className":3093},[644,645],[574,3095,3097,3124],{"className":3096},[649],[574,3098,3100,3112],{"className":3099,"style":2533},[653],[574,3101,3103,3106],{"className":3102,"style":1732},[1731],[574,3104],{"className":3105,"style":1675},[661],[574,3107,3109],{"className":3108,"style":1739},[631,669],[574,3110,841],{"className":3111},[631,669],[574,3113,3114,3117],{"style":2548},[574,3115],{"className":3116,"style":1675},[661],[574,3118,3120],{"className":3119,"style":1753},[1752,669],[1755,3121,3122],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,3123],{"d":1765},[574,3125,677],{"className":3126},[676],[574,3128,3130],{"className":3129},[649],[574,3131,3133],{"className":3132,"style":2568},[653],[574,3134],{},[574,3136,3137,3140],{"style":1684},[574,3138],{"className":3139,"style":1675},[661],[574,3141],{"className":3142,"style":1692},[1691],[574,3144,3145,3148],{"style":2581},[574,3146],{"className":3147,"style":1675},[661],[574,3149,3151],{"className":3150},[666,667,668,669],[574,3152,3154],{"className":3153},[631,669],[574,3155,3157,3160],{"className":3156},[631,669],[574,3158,1560],{"className":3159},[631,669],[574,3161,3163],{"className":3162},[640],[574,3164,3166],{"className":3165},[644],[574,3167,3169],{"className":3168},[649],[574,3170,3173],{"className":3171,"style":3172},[653],"height:0.7385em;",[574,3174,3176,3180],{"style":3175},"top:-2.931em;margin-right:0.0714em;",[574,3177],{"className":3178,"style":3179},[661],"height:2.5em;",[574,3181,3185],{"className":3182},[666,3183,3184,669],"reset-size3","size1",[574,3186,1012],{"className":3187},[631,635,669],[574,3189,677],{"className":3190},[676],[574,3192,3194],{"className":3193},[649],[574,3195,3197],{"className":3196,"style":2603},[653],[574,3198],{},[574,3200],{"className":3201},[1793,1655],".",[2829,3204,3205,3206,3411,3412,3202],{},"Die Fibonacci-Zahlen wachsen exponentiell, und der Quotient ",[574,3207,3209,3241],{"className":3208},[577],[574,3210,3212],{"className":3211},[581],[583,3213,3214],{"xmlns":585},[587,3215,3216,3238],{},[590,3217,3218],{},[1564,3219,3220,3232],{},[593,3221,3222,3224],{},[596,3223,598],{},[590,3225,3226,3228,3230],{},[596,3227,1012],{},[604,3229,1219],{},[600,3231,728],{},[593,3233,3234,3236],{},[596,3235,598],{},[596,3237,1012],{},[610,3239,3240],{"encoding":612},"\\frac{F_{n+1}}{F_n}",[574,3242,3244],{"className":3243,"ariaHidden":618},[617],[574,3245,3247,3251],{"className":3246},[622],[574,3248],{"className":3249,"style":3250},[626],"height:1.3752em;vertical-align:-0.4451em;",[574,3252,3254,3257,3408],{"className":3253},[631],[574,3255],{"className":3256},[1654,1655],[574,3258,3260],{"className":3259},[1564],[574,3261,3263,3399],{"className":3262},[644,645],[574,3264,3266,3396],{"className":3265},[649],[574,3267,3270,3325,3333],{"className":3268,"style":3269},[653],"height:0.9301em;",[574,3271,3273,3276],{"style":3272},"top:-2.655em;",[574,3274],{"className":3275,"style":1675},[661],[574,3277,3279],{"className":3278},[666,667,668,669],[574,3280,3282],{"className":3281},[631,669],[574,3283,3285,3288],{"className":3284},[631,669],[574,3286,598],{"className":3287,"style":636},[631,635,669],[574,3289,3291],{"className":3290},[640],[574,3292,3294,3316],{"className":3293},[644,645],[574,3295,3297,3313],{"className":3296},[649],[574,3298,3301],{"className":3299,"style":3300},[653],"height:0.1645em;",[574,3302,3304,3307],{"style":3303},"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;",[574,3305],{"className":3306,"style":3179},[661],[574,3308,3310],{"className":3309},[666,3183,3184,669],[574,3311,1012],{"className":3312},[631,635,669],[574,3314,677],{"className":3315},[676],[574,3317,3319],{"className":3318},[649],[574,3320,3323],{"className":3321,"style":3322},[653],"height:0.143em;",[574,3324],{},[574,3326,3327,3330],{"style":1684},[574,3328],{"className":3329,"style":1675},[661],[574,3331],{"className":3332,"style":1692},[1691],[574,3334,3336,3339],{"style":3335},"top:-3.4518em;",[574,3337],{"className":3338,"style":1675},[661],[574,3340,3342],{"className":3341},[666,667,668,669],[574,3343,3345],{"className":3344},[631,669],[574,3346,3348,3351],{"className":3347},[631,669],[574,3349,598],{"className":3350,"style":636},[631,635,669],[574,3352,3354],{"className":3353},[640],[574,3355,3357,3387],{"className":3356},[644,645],[574,3358,3360,3384],{"className":3359},[649],[574,3361,3364],{"className":3362,"style":3363},[653],"height:0.3173em;",[574,3365,3366,3369],{"style":3303},[574,3367],{"className":3368,"style":3179},[661],[574,3370,3372],{"className":3371},[666,3183,3184,669],[574,3373,3375,3378,3381],{"className":3374},[631,669],[574,3376,1012],{"className":3377},[631,635,669],[574,3379,1219],{"className":3380},[1293,669],[574,3382,728],{"className":3383},[631,669],[574,3385,677],{"className":3386},[676],[574,3388,3390],{"className":3389},[649],[574,3391,3394],{"className":3392,"style":3393},[653],"height:0.2025em;",[574,3395],{},[574,3397,677],{"className":3398},[676],[574,3400,3402],{"className":3401},[649],[574,3403,3406],{"className":3404,"style":3405},[653],"height:0.4451em;",[574,3407],{},[574,3409],{"className":3410},[1793,1655]," strebt gegen den goldenen Schnitt ",[574,3413,3415,3429],{"className":3414},[577],[574,3416,3418],{"className":3417},[581],[583,3419,3420],{"xmlns":585},[587,3421,3422,3426],{},[590,3423,3424],{},[596,3425,1560],{"mathvariant":1559},[610,3427,3428],{"encoding":612},"\\Phi",[574,3430,3432],{"className":3431,"ariaHidden":618},[617],[574,3433,3435,3438],{"className":3434},[622],[574,3436],{"className":3437,"style":1628},[626],[574,3439,1560],{"className":3440},[631],[560,3442,3444],{"id":3443},"beispiele","Beispiele",[565,3446,3447,3521],{},[574,3448,3450,3469],{"className":3449},[577],[574,3451,3453],{"className":3452},[581],[583,3454,3455],{"xmlns":585},[587,3456,3457,3466],{},[590,3458,3459],{},[593,3460,3461,3463],{},[596,3462,598],{},[600,3464,3465],{},"10",[610,3467,3468],{"encoding":612},"F_{10}",[574,3470,3472],{"className":3471,"ariaHidden":618},[617],[574,3473,3475,3478],{"className":3474},[622],[574,3476],{"className":3477,"style":627},[626],[574,3479,3481,3484],{"className":3480},[631],[574,3482,598],{"className":3483,"style":636},[631,635],[574,3485,3487],{"className":3486},[640],[574,3488,3490,3513],{"className":3489},[644,645],[574,3491,3493,3510],{"className":3492},[649],[574,3494,3496],{"className":3495,"style":654},[653],[574,3497,3498,3501],{"style":657},[574,3499],{"className":3500,"style":662},[661],[574,3502,3504],{"className":3503},[666,667,668,669],[574,3505,3507],{"className":3506},[631,669],[574,3508,3465],{"className":3509},[631,669],[574,3511,677],{"className":3512},[676],[574,3514,3516],{"className":3515},[649],[574,3517,3519],{"className":3518,"style":684},[653],[574,3520],{},":",[574,3523,3525],{"className":3524},[1543],[574,3526,3528,3582],{"className":3527},[577],[574,3529,3531],{"className":3530},[581],[583,3532,3533],{"xmlns":585,"display":1552},[587,3534,3535,3579],{},[590,3536,3537,3543,3545,3553,3575,3577],{},[593,3538,3539,3541],{},[596,3540,598],{},[600,3542,3465],{},[604,3544,606],{},[1564,3546,3547,3549],{},[600,3548,728],{},[1573,3550,3551],{},[600,3552,841],{},[590,3554,3555,3558,3564,3566,3572],{},[604,3556,3557],{"fence":618},"(",[1091,3559,3560,3562],{},[596,3561,1560],{"mathvariant":1559},[600,3563,3465],{},[604,3565,1242],{},[1091,3567,3568,3570],{},[596,3569,1592],{},[600,3571,3465],{},[604,3573,3574],{"fence":618},")",[604,3576,606],{},[600,3578,866],{},[610,3580,3581],{"encoding":612},"F_{10} = \\frac{1}{\\sqrt{5}} \\left( \\Phi^{10} - \\psi^{10} \\right) = 55",[574,3583,3585,3643,3864],{"className":3584,"ariaHidden":618},[617],[574,3586,3588,3591,3634,3637,3640],{"className":3587},[622],[574,3589],{"className":3590,"style":627},[626],[574,3592,3594,3597],{"className":3593},[631],[574,3595,598],{"className":3596,"style":636},[631,635],[574,3598,3600],{"className":3599},[640],[574,3601,3603,3626],{"className":3602},[644,645],[574,3604,3606,3623],{"className":3605},[649],[574,3607,3609],{"className":3608,"style":654},[653],[574,3610,3611,3614],{"style":657},[574,3612],{"className":3613,"style":662},[661],[574,3615,3617],{"className":3616},[666,667,668,669],[574,3618,3620],{"className":3619},[631,669],[574,3621,3465],{"className":3622},[631,669],[574,3624,677],{"className":3625},[676],[574,3627,3629],{"className":3628},[649],[574,3630,3632],{"className":3631,"style":684},[653],[574,3633],{},[574,3635],{"className":3636,"style":691},[690],[574,3638,606],{"className":3639},[695],[574,3641],{"className":3642,"style":691},[690],[574,3644,3646,3650,3759,3762,3855,3858,3861],{"className":3645},[622],[574,3647],{"className":3648,"style":3649},[626],"height:2.2514em;vertical-align:-0.93em;",[574,3651,3653,3656,3756],{"className":3652},[631],[574,3654],{"className":3655},[1654,1655],[574,3657,3659],{"className":3658},[1564],[574,3660,3662,3747],{"className":3661},[644,645],[574,3663,3665,3744],{"className":3664},[649],[574,3666,3669,3725,3733],{"className":3667,"style":3668},[653],"height:1.3214em;",[574,3670,3672,3675],{"style":3671},"top:-2.2028em;",[574,3673],{"className":3674,"style":1675},[661],[574,3676,3678],{"className":3677},[631],[574,3679,3681],{"className":3680},[631,1717],[574,3682,3684,3717],{"className":3683},[644,645],[574,3685,3687,3714],{"className":3686},[649],[574,3688,3690,3702],{"className":3689,"style":1727},[653],[574,3691,3693,3696],{"className":3692,"style":1732},[1731],[574,3694],{"className":3695,"style":1675},[661],[574,3697,3699],{"className":3698,"style":1739},[631],[574,3700,841],{"className":3701},[631],[574,3703,3704,3707],{"style":1745},[574,3705],{"className":3706,"style":1675},[661],[574,3708,3710],{"className":3709,"style":1753},[1752],[1755,3711,3712],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,3713],{"d":1765},[574,3715,677],{"className":3716},[676],[574,3718,3720],{"className":3719},[649],[574,3721,3723],{"className":3722,"style":1775},[653],[574,3724],{},[574,3726,3727,3730],{"style":1684},[574,3728],{"className":3729,"style":1675},[661],[574,3731],{"className":3732,"style":1692},[1691],[574,3734,3735,3738],{"style":1695},[574,3736],{"className":3737,"style":1675},[661],[574,3739,3741],{"className":3740},[631],[574,3742,728],{"className":3743},[631],[574,3745,677],{"className":3746},[676],[574,3748,3750],{"className":3749},[649],[574,3751,3754],{"className":3752,"style":3753},[653],"height:0.93em;",[574,3755],{},[574,3757],{"className":3758},[1793,1655],[574,3760],{"className":3761,"style":895},[690],[574,3763,3765,3774,3808,3811,3814,3817,3849],{"className":3764},[989],[574,3766,3770],{"className":3767,"style":3769},[1654,3768],"delimcenter","top:0em;",[574,3771,3557],{"className":3772},[3773,3184],"delimsizing",[574,3775,3777,3780],{"className":3776},[631],[574,3778,1560],{"className":3779},[631],[574,3781,3783],{"className":3782},[640],[574,3784,3786],{"className":3785},[644],[574,3787,3789],{"className":3788},[649],[574,3790,3793],{"className":3791,"style":3792},[653],"height:0.8641em;",[574,3794,3796,3799],{"style":3795},"top:-3.113em;margin-right:0.05em;",[574,3797],{"className":3798,"style":662},[661],[574,3800,3802],{"className":3801},[666,667,668,669],[574,3803,3805],{"className":3804},[631,669],[574,3806,3465],{"className":3807},[631,669],[574,3809],{"className":3810,"style":1367},[690],[574,3812,1242],{"className":3813},[1293],[574,3815],{"className":3816,"style":1367},[690],[574,3818,3820,3823],{"className":3819},[631],[574,3821,1592],{"className":3822,"style":1836},[631,635],[574,3824,3826],{"className":3825},[640],[574,3827,3829],{"className":3828},[644],[574,3830,3832],{"className":3831},[649],[574,3833,3835],{"className":3834,"style":3792},[653],[574,3836,3837,3840],{"style":3795},[574,3838],{"className":3839,"style":662},[661],[574,3841,3843],{"className":3842},[666,667,668,669],[574,3844,3846],{"className":3845},[631,669],[574,3847,3465],{"className":3848},[631,669],[574,3850,3852],{"className":3851,"style":3769},[1793,3768],[574,3853,3574],{"className":3854},[3773,3184],[574,3856],{"className":3857,"style":691},[690],[574,3859,606],{"className":3860},[695],[574,3862],{"className":3863,"style":691},[690],[574,3865,3867,3870],{"className":3866},[622],[574,3868],{"className":3869,"style":705},[626],[574,3871,866],{"className":3872},[631],[565,3874,3875,3949,3950,4164,4165,3202],{},[574,3876,3878,3897],{"className":3877},[577],[574,3879,3881],{"className":3880},[581],[583,3882,3883],{"xmlns":585},[587,3884,3885,3894],{},[590,3886,3887],{},[593,3888,3889,3891],{},[596,3890,598],{},[600,3892,3893],{},"20",[610,3895,3896],{"encoding":612},"F_{20}",[574,3898,3900],{"className":3899,"ariaHidden":618},[617],[574,3901,3903,3906],{"className":3902},[622],[574,3904],{"className":3905,"style":627},[626],[574,3907,3909,3912],{"className":3908},[631],[574,3910,598],{"className":3911,"style":636},[631,635],[574,3913,3915],{"className":3914},[640],[574,3916,3918,3941],{"className":3917},[644,645],[574,3919,3921,3938],{"className":3920},[649],[574,3922,3924],{"className":3923,"style":654},[653],[574,3925,3926,3929],{"style":657},[574,3927],{"className":3928,"style":662},[661],[574,3930,3932],{"className":3931},[666,667,668,669],[574,3933,3935],{"className":3934},[631,669],[574,3936,3893],{"className":3937},[631,669],[574,3939,677],{"className":3940},[676],[574,3942,3944],{"className":3943},[649],[574,3945,3947],{"className":3946,"style":684},[653],[574,3948],{}," mit der Rundungsformel: ",[574,3951,3953,3982],{"className":3952},[577],[574,3954,3956],{"className":3955},[581],[583,3957,3958],{"xmlns":585},[587,3959,3960,3979],{},[590,3961,3962,3974,3976],{},[1564,3963,3964,3970],{},[1091,3965,3966,3968],{},[596,3967,1560],{"mathvariant":1559},[600,3969,3893],{},[1573,3971,3972],{},[600,3973,841],{},[604,3975,1581],{},[600,3977,3978],{},"6765,00003",[610,3980,3981],{"encoding":612},"\\frac{\\Phi^{20}}{\\sqrt{5}} \\approx 6765{,}00003",[574,3983,3985,4144],{"className":3984,"ariaHidden":618},[617],[574,3986,3988,3992,4135,4138,4141],{"className":3987},[622],[574,3989],{"className":3990,"style":3991},[626],"height:1.5559em;vertical-align:-0.538em;",[574,3993,3995,3998,4132],{"className":3994},[631],[574,3996],{"className":3997},[1654,1655],[574,3999,4001],{"className":4000},[1564],[574,4002,4004,4124],{"className":4003},[644,645],[574,4005,4007,4121],{"className":4006},[649],[574,4008,4011,4069,4077],{"className":4009,"style":4010},[653],"height:1.0179em;",[574,4012,4013,4016],{"style":2511},[574,4014],{"className":4015,"style":1675},[661],[574,4017,4019],{"className":4018},[666,667,668,669],[574,4020,4022],{"className":4021},[631,669],[574,4023,4025],{"className":4024},[631,1717,669],[574,4026,4028,4061],{"className":4027},[644,645],[574,4029,4031,4058],{"className":4030},[649],[574,4032,4034,4046],{"className":4033,"style":2533},[653],[574,4035,4037,4040],{"className":4036,"style":1732},[1731],[574,4038],{"className":4039,"style":1675},[661],[574,4041,4043],{"className":4042,"style":1739},[631,669],[574,4044,841],{"className":4045},[631,669],[574,4047,4048,4051],{"style":2548},[574,4049],{"className":4050,"style":1675},[661],[574,4052,4054],{"className":4053,"style":1753},[1752,669],[1755,4055,4056],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,4057],{"d":1765},[574,4059,677],{"className":4060},[676],[574,4062,4064],{"className":4063},[649],[574,4065,4067],{"className":4066,"style":2568},[653],[574,4068],{},[574,4070,4071,4074],{"style":1684},[574,4072],{"className":4073,"style":1675},[661],[574,4075],{"className":4076,"style":1692},[1691],[574,4078,4079,4082],{"style":2581},[574,4080],{"className":4081,"style":1675},[661],[574,4083,4085],{"className":4084},[666,667,668,669],[574,4086,4088],{"className":4087},[631,669],[574,4089,4091,4094],{"className":4090},[631,669],[574,4092,1560],{"className":4093},[631,669],[574,4095,4097],{"className":4096},[640],[574,4098,4100],{"className":4099},[644],[574,4101,4103],{"className":4102},[649],[574,4104,4107],{"className":4105,"style":4106},[653],"height:0.8913em;",[574,4108,4109,4112],{"style":3175},[574,4110],{"className":4111,"style":3179},[661],[574,4113,4115],{"className":4114},[666,3183,3184,669],[574,4116,4118],{"className":4117},[631,669],[574,4119,3893],{"className":4120},[631,669],[574,4122,677],{"className":4123},[676],[574,4125,4127],{"className":4126},[649],[574,4128,4130],{"className":4129,"style":2603},[653],[574,4131],{},[574,4133],{"className":4134},[1793,1655],[574,4136],{"className":4137,"style":691},[690],[574,4139,1581],{"className":4140},[695],[574,4142],{"className":4143,"style":691},[690],[574,4145,4147,4150,4154,4160],{"className":4146},[622],[574,4148],{"className":4149,"style":884},[626],[574,4151,4153],{"className":4152},[631],"6765",[574,4155,4157],{"className":4156},[631],[574,4158,820],{"className":4159},[891],[574,4161,4163],{"className":4162},[631],"00003",", also ",[574,4166,4168,4190],{"className":4167},[577],[574,4169,4171],{"className":4170},[581],[583,4172,4173],{"xmlns":585},[587,4174,4175,4187],{},[590,4176,4177,4183,4185],{},[593,4178,4179,4181],{},[596,4180,598],{},[600,4182,3893],{},[604,4184,606],{},[600,4186,4153],{},[610,4188,4189],{"encoding":612},"F_{20} = 6765",[574,4191,4193,4251],{"className":4192,"ariaHidden":618},[617],[574,4194,4196,4199,4242,4245,4248],{"className":4195},[622],[574,4197],{"className":4198,"style":627},[626],[574,4200,4202,4205],{"className":4201},[631],[574,4203,598],{"className":4204,"style":636},[631,635],[574,4206,4208],{"className":4207},[640],[574,4209,4211,4234],{"className":4210},[644,645],[574,4212,4214,4231],{"className":4213},[649],[574,4215,4217],{"className":4216,"style":654},[653],[574,4218,4219,4222],{"style":657},[574,4220],{"className":4221,"style":662},[661],[574,4223,4225],{"className":4224},[666,667,668,669],[574,4226,4228],{"className":4227},[631,669],[574,4229,3893],{"className":4230},[631,669],[574,4232,677],{"className":4233},[676],[574,4235,4237],{"className":4236},[649],[574,4238,4240],{"className":4239,"style":684},[653],[574,4241],{},[574,4243],{"className":4244,"style":691},[690],[574,4246,606],{"className":4247},[695],[574,4249],{"className":4250,"style":691},[690],[574,4252,4254,4257],{"className":4253},[622],[574,4255],{"className":4256,"style":705},[626],[574,4258,4153],{"className":4259},[631],[565,4261,4262,4263,4580,4581,3202],{},"Quotient: ",[574,4264,4266,4307],{"className":4265},[577],[574,4267,4269],{"className":4268},[581],[583,4270,4271],{"xmlns":585},[587,4272,4273,4304],{},[590,4274,4275,4290,4292,4299,4301],{},[1564,4276,4277,4284],{},[593,4278,4279,4281],{},[596,4280,598],{},[600,4282,4283],{},"11",[593,4285,4286,4288],{},[596,4287,598],{},[600,4289,3465],{},[604,4291,606],{},[1564,4293,4294,4297],{},[600,4295,4296],{},"89",[600,4298,866],{},[604,4300,1581],{},[600,4302,4303],{},"1,6182",[610,4305,4306],{"encoding":612},"\\frac{F_{11}}{F_{10}} = \\frac{89}{55} \\approx 1{,}6182",[574,4308,4310,4476,4561],{"className":4309,"ariaHidden":618},[617],[574,4311,4313,4317,4467,4470,4473],{"className":4312},[622],[574,4314],{"className":4315,"style":4316},[626],"height:1.3335em;vertical-align:-0.4451em;",[574,4318,4320,4323,4464],{"className":4319},[631],[574,4321],{"className":4322},[1654,1655],[574,4324,4326],{"className":4325},[1564],[574,4327,4329,4456],{"className":4328},[644,645],[574,4330,4332,4453],{"className":4331},[649],[574,4333,4336,4390,4398],{"className":4334,"style":4335},[653],"height:0.8884em;",[574,4337,4338,4341],{"style":3272},[574,4339],{"className":4340,"style":1675},[661],[574,4342,4344],{"className":4343},[666,667,668,669],[574,4345,4347],{"className":4346},[631,669],[574,4348,4350,4353],{"className":4349},[631,669],[574,4351,598],{"className":4352,"style":636},[631,635,669],[574,4354,4356],{"className":4355},[640],[574,4357,4359,4382],{"className":4358},[644,645],[574,4360,4362,4379],{"className":4361},[649],[574,4363,4365],{"className":4364,"style":3363},[653],[574,4366,4367,4370],{"style":3303},[574,4368],{"className":4369,"style":3179},[661],[574,4371,4373],{"className":4372},[666,3183,3184,669],[574,4374,4376],{"className":4375},[631,669],[574,4377,3465],{"className":4378},[631,669],[574,4380,677],{"className":4381},[676],[574,4383,4385],{"className":4384},[649],[574,4386,4388],{"className":4387,"style":3322},[653],[574,4389],{},[574,4391,4392,4395],{"style":1684},[574,4393],{"className":4394,"style":1675},[661],[574,4396],{"className":4397,"style":1692},[1691],[574,4399,4401,4404],{"style":4400},"top:-3.4101em;",[574,4402],{"className":4403,"style":1675},[661],[574,4405,4407],{"className":4406},[666,667,668,669],[574,4408,4410],{"className":4409},[631,669],[574,4411,4413,4416],{"className":4412},[631,669],[574,4414,598],{"className":4415,"style":636},[631,635,669],[574,4417,4419],{"className":4418},[640],[574,4420,4422,4445],{"className":4421},[644,645],[574,4423,4425,4442],{"className":4424},[649],[574,4426,4428],{"className":4427,"style":3363},[653],[574,4429,4430,4433],{"style":3303},[574,4431],{"className":4432,"style":3179},[661],[574,4434,4436],{"className":4435},[666,3183,3184,669],[574,4437,4439],{"className":4438},[631,669],[574,4440,4283],{"className":4441},[631,669],[574,4443,677],{"className":4444},[676],[574,4446,4448],{"className":4447},[649],[574,4449,4451],{"className":4450,"style":3322},[653],[574,4452],{},[574,4454,677],{"className":4455},[676],[574,4457,4459],{"className":4458},[649],[574,4460,4462],{"className":4461,"style":3405},[653],[574,4463],{},[574,4465],{"className":4466},[1793,1655],[574,4468],{"className":4469,"style":691},[690],[574,4471,606],{"className":4472},[695],[574,4474],{"className":4475,"style":691},[690],[574,4477,4479,4483,4552,4555,4558],{"className":4478},[622],[574,4480],{"className":4481,"style":4482},[626],"height:1.1901em;vertical-align:-0.345em;",[574,4484,4486,4489,4549],{"className":4485},[631],[574,4487],{"className":4488},[1654,1655],[574,4490,4492],{"className":4491},[1564],[574,4493,4495,4540],{"className":4494},[644,645],[574,4496,4498,4537],{"className":4497},[649],[574,4499,4501,4515,4523],{"className":4500,"style":2508},[653],[574,4502,4503,4506],{"style":3272},[574,4504],{"className":4505,"style":1675},[661],[574,4507,4509],{"className":4508},[666,667,668,669],[574,4510,4512],{"className":4511},[631,669],[574,4513,866],{"className":4514},[631,669],[574,4516,4517,4520],{"style":1684},[574,4518],{"className":4519,"style":1675},[661],[574,4521],{"className":4522,"style":1692},[1691],[574,4524,4525,4528],{"style":2581},[574,4526],{"className":4527,"style":1675},[661],[574,4529,4531],{"className":4530},[666,667,668,669],[574,4532,4534],{"className":4533},[631,669],[574,4535,4296],{"className":4536},[631,669],[574,4538,677],{"className":4539},[676],[574,4541,4543],{"className":4542},[649],[574,4544,4547],{"className":4545,"style":4546},[653],"height:0.345em;",[574,4548],{},[574,4550],{"className":4551},[1793,1655],[574,4553],{"className":4554,"style":691},[690],[574,4556,1581],{"className":4557},[695],[574,4559],{"className":4560,"style":691},[690],[574,4562,4564,4567,4570,4576],{"className":4563},[622],[574,4565],{"className":4566,"style":884},[626],[574,4568,728],{"className":4569},[631],[574,4571,4573],{"className":4572},[631],[574,4574,820],{"className":4575},[891],[574,4577,4579],{"className":4578},[631],"6182",", sehr nahe an ",[574,4582,4584,4603],{"className":4583},[577],[574,4585,4587],{"className":4586},[581],[583,4588,4589],{"xmlns":585},[587,4590,4591,4600],{},[590,4592,4593,4595,4597],{},[596,4594,1560],{"mathvariant":1559},[604,4596,1581],{},[600,4598,4599],{},"1,6180",[610,4601,4602],{"encoding":612},"\\Phi \\approx 1{,}6180",[574,4604,4606,4624],{"className":4605,"ariaHidden":618},[617],[574,4607,4609,4612,4615,4618,4621],{"className":4608},[622],[574,4610],{"className":4611,"style":1628},[626],[574,4613,1560],{"className":4614},[631],[574,4616],{"className":4617,"style":691},[690],[574,4619,1581],{"className":4620},[695],[574,4622],{"className":4623,"style":691},[690],[574,4625,4627,4630,4633,4639],{"className":4626},[622],[574,4628],{"className":4629,"style":884},[626],[574,4631,728],{"className":4632},[631],[574,4634,4636],{"className":4635},[631],[574,4637,820],{"className":4638},[891],[574,4640,4642],{"className":4641},[631],"6180",[560,4644,4646],{"id":4645},"typische-fehler","Typische Fehler",[2826,4648,4649,4888,5143],{},[2829,4650,4651,1433,4654,4827,4828,4887],{},[569,4652,4653],{},"Den zweiten Summanden weglassen, ohne zu runden.",[574,4655,4657,4680],{"className":4656},[577],[574,4658,4660],{"className":4659},[581],[583,4661,4662],{"xmlns":585},[587,4663,4664,4678],{},[590,4665,4666],{},[1564,4667,4668,4674],{},[1091,4669,4670,4672],{},[596,4671,1560],{"mathvariant":1559},[596,4673,1012],{},[1573,4675,4676],{},[600,4677,841],{},[610,4679,3047],{"encoding":612},[574,4681,4683],{"className":4682,"ariaHidden":618},[617],[574,4684,4686,4689],{"className":4685},[622],[574,4687],{"className":4688,"style":3057},[626],[574,4690,4692,4695,4824],{"className":4691},[631],[574,4693],{"className":4694},[1654,1655],[574,4696,4698],{"className":4697},[1564],[574,4699,4701,4816],{"className":4700},[644,645],[574,4702,4704,4813],{"className":4703},[649],[574,4705,4707,4765,4773],{"className":4706,"style":3076},[653],[574,4708,4709,4712],{"style":2511},[574,4710],{"className":4711,"style":1675},[661],[574,4713,4715],{"className":4714},[666,667,668,669],[574,4716,4718],{"className":4717},[631,669],[574,4719,4721],{"className":4720},[631,1717,669],[574,4722,4724,4757],{"className":4723},[644,645],[574,4725,4727,4754],{"className":4726},[649],[574,4728,4730,4742],{"className":4729,"style":2533},[653],[574,4731,4733,4736],{"className":4732,"style":1732},[1731],[574,4734],{"className":4735,"style":1675},[661],[574,4737,4739],{"className":4738,"style":1739},[631,669],[574,4740,841],{"className":4741},[631,669],[574,4743,4744,4747],{"style":2548},[574,4745],{"className":4746,"style":1675},[661],[574,4748,4750],{"className":4749,"style":1753},[1752,669],[1755,4751,4752],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,4753],{"d":1765},[574,4755,677],{"className":4756},[676],[574,4758,4760],{"className":4759},[649],[574,4761,4763],{"className":4762,"style":2568},[653],[574,4764],{},[574,4766,4767,4770],{"style":1684},[574,4768],{"className":4769,"style":1675},[661],[574,4771],{"className":4772,"style":1692},[1691],[574,4774,4775,4778],{"style":2581},[574,4776],{"className":4777,"style":1675},[661],[574,4779,4781],{"className":4780},[666,667,668,669],[574,4782,4784],{"className":4783},[631,669],[574,4785,4787,4790],{"className":4786},[631,669],[574,4788,1560],{"className":4789},[631,669],[574,4791,4793],{"className":4792},[640],[574,4794,4796],{"className":4795},[644],[574,4797,4799],{"className":4798},[649],[574,4800,4802],{"className":4801,"style":3172},[653],[574,4803,4804,4807],{"style":3175},[574,4805],{"className":4806,"style":3179},[661],[574,4808,4810],{"className":4809},[666,3183,3184,669],[574,4811,1012],{"className":4812},[631,635,669],[574,4814,677],{"className":4815},[676],[574,4817,4819],{"className":4818},[649],[574,4820,4822],{"className":4821,"style":2603},[653],[574,4823],{},[574,4825],{"className":4826},[1793,1655]," ist nie exakt ganzzahlig. Ohne ",[574,4829,4831,4849],{"className":4830},[577],[574,4832,4834],{"className":4833},[581],[583,4835,4836],{"xmlns":585},[587,4837,4838,4846],{},[590,4839,4840],{},[1091,4841,4842,4844],{},[596,4843,1592],{},[596,4845,1012],{},[610,4847,4848],{"encoding":612},"\\psi^n",[574,4850,4852],{"className":4851,"ariaHidden":618},[617],[574,4853,4855,4858],{"className":4854},[622],[574,4856],{"className":4857,"style":1809},[626],[574,4859,4861,4864],{"className":4860},[631],[574,4862,1592],{"className":4863,"style":1836},[631,635],[574,4865,4867],{"className":4866},[640],[574,4868,4870],{"className":4869},[644],[574,4871,4873],{"className":4872},[649],[574,4874,4876],{"className":4875,"style":1165},[653],[574,4877,4878,4881],{"style":1186},[574,4879],{"className":4880,"style":662},[661],[574,4882,4884],{"className":4883},[666,667,668,669],[574,4885,1012],{"className":4886},[631,635,669]," muss man auf die nächste ganze Zahl runden.",[2829,4889,4890,4893,4894,5049,5050,5142],{},[569,4891,4892],{},"Andere Startwerte verwenden."," Beginnt die Folge mit ",[574,4895,4897,4927],{"className":4896},[577],[574,4898,4900],{"className":4899},[581],[583,4901,4902],{"xmlns":585},[587,4903,4904,4924],{},[590,4905,4906,4912,4914,4920,4922],{},[593,4907,4908,4910],{},[596,4909,598],{},[600,4911,728],{},[604,4913,606],{},[593,4915,4916,4918],{},[596,4917,598],{},[600,4919,831],{},[604,4921,606],{},[600,4923,728],{},[610,4925,4926],{"encoding":612},"F_1 = F_2 = 1",[574,4928,4930,4985,5040],{"className":4929,"ariaHidden":618},[617],[574,4931,4933,4936,4976,4979,4982],{"className":4932},[622],[574,4934],{"className":4935,"style":627},[626],[574,4937,4939,4942],{"className":4938},[631],[574,4940,598],{"className":4941,"style":636},[631,635],[574,4943,4945],{"className":4944},[640],[574,4946,4948,4968],{"className":4947},[644,645],[574,4949,4951,4965],{"className":4950},[649],[574,4952,4954],{"className":4953,"style":654},[653],[574,4955,4956,4959],{"style":657},[574,4957],{"className":4958,"style":662},[661],[574,4960,4962],{"className":4961},[666,667,668,669],[574,4963,728],{"className":4964},[631,669],[574,4966,677],{"className":4967},[676],[574,4969,4971],{"className":4970},[649],[574,4972,4974],{"className":4973,"style":684},[653],[574,4975],{},[574,4977],{"className":4978,"style":691},[690],[574,4980,606],{"className":4981},[695],[574,4983],{"className":4984,"style":691},[690],[574,4986,4988,4991,5031,5034,5037],{"className":4987},[622],[574,4989],{"className":4990,"style":627},[626],[574,4992,4994,4997],{"className":4993},[631],[574,4995,598],{"className":4996,"style":636},[631,635],[574,4998,5000],{"className":4999},[640],[574,5001,5003,5023],{"className":5002},[644,645],[574,5004,5006,5020],{"className":5005},[649],[574,5007,5009],{"className":5008,"style":654},[653],[574,5010,5011,5014],{"style":657},[574,5012],{"className":5013,"style":662},[661],[574,5015,5017],{"className":5016},[666,667,668,669],[574,5018,831],{"className":5019},[631,669],[574,5021,677],{"className":5022},[676],[574,5024,5026],{"className":5025},[649],[574,5027,5029],{"className":5028,"style":684},[653],[574,5030],{},[574,5032],{"className":5033,"style":691},[690],[574,5035,606],{"className":5036},[695],[574,5038],{"className":5039,"style":691},[690],[574,5041,5043,5046],{"className":5042},[622],[574,5044],{"className":5045,"style":705},[626],[574,5047,728],{"className":5048},[631],", stimmt die Formel mit derselben Nummerierung. Wer aber ",[574,5051,5053,5075],{"className":5052},[577],[574,5054,5056],{"className":5055},[581],[583,5057,5058],{"xmlns":585},[587,5059,5060,5072],{},[590,5061,5062,5068,5070],{},[593,5063,5064,5066],{},[596,5065,598],{},[600,5067,602],{},[604,5069,606],{},[600,5071,728],{},[610,5073,5074],{"encoding":612},"F_0 = 1",[574,5076,5078,5133],{"className":5077,"ariaHidden":618},[617],[574,5079,5081,5084,5124,5127,5130],{"className":5080},[622],[574,5082],{"className":5083,"style":627},[626],[574,5085,5087,5090],{"className":5086},[631],[574,5088,598],{"className":5089,"style":636},[631,635],[574,5091,5093],{"className":5092},[640],[574,5094,5096,5116],{"className":5095},[644,645],[574,5097,5099,5113],{"className":5098},[649],[574,5100,5102],{"className":5101,"style":654},[653],[574,5103,5104,5107],{"style":657},[574,5105],{"className":5106,"style":662},[661],[574,5108,5110],{"className":5109},[666,667,668,669],[574,5111,602],{"className":5112},[631,669],[574,5114,677],{"className":5115},[676],[574,5117,5119],{"className":5118},[649],[574,5120,5122],{"className":5121,"style":684},[653],[574,5123],{},[574,5125],{"className":5126,"style":691},[690],[574,5128,606],{"className":5129},[695],[574,5131],{"className":5132,"style":691},[690],[574,5134,5136,5139],{"className":5135},[622],[574,5137],{"className":5138,"style":705},[626],[574,5140,728],{"className":5141},[631]," setzt, verschiebt den Index um eins.",[2829,5144,5145,1433,5178,5206,5207,5265,5266,5295,5296,5469,5470,5539],{},[569,5146,5147,5148,5177],{},"Vorzeichen von ",[574,5149,5151,5165],{"className":5150},[577],[574,5152,5154],{"className":5153},[581],[583,5155,5156],{"xmlns":585},[587,5157,5158,5162],{},[590,5159,5160],{},[596,5161,1592],{},[610,5163,5164],{"encoding":612},"\\psi",[574,5166,5168],{"className":5167,"ariaHidden":618},[617],[574,5169,5171,5174],{"className":5170},[622],[574,5172],{"className":5173,"style":1809},[626],[574,5175,1592],{"className":5176,"style":1836},[631,635]," übersehen.",[574,5179,5181,5194],{"className":5180},[577],[574,5182,5184],{"className":5183},[581],[583,5185,5186],{"xmlns":585},[587,5187,5188,5192],{},[590,5189,5190],{},[596,5191,1592],{},[610,5193,5164],{"encoding":612},[574,5195,5197],{"className":5196,"ariaHidden":618},[617],[574,5198,5200,5203],{"className":5199},[622],[574,5201],{"className":5202,"style":1809},[626],[574,5204,1592],{"className":5205,"style":1836},[631,635]," ist negativ, daher wechselt ",[574,5208,5210,5227],{"className":5209},[577],[574,5211,5213],{"className":5212},[581],[583,5214,5215],{"xmlns":585},[587,5216,5217,5225],{},[590,5218,5219],{},[1091,5220,5221,5223],{},[596,5222,1592],{},[596,5224,1012],{},[610,5226,4848],{"encoding":612},[574,5228,5230],{"className":5229,"ariaHidden":618},[617],[574,5231,5233,5236],{"className":5232},[622],[574,5234],{"className":5235,"style":1809},[626],[574,5237,5239,5242],{"className":5238},[631],[574,5240,1592],{"className":5241,"style":1836},[631,635],[574,5243,5245],{"className":5244},[640],[574,5246,5248],{"className":5247},[644],[574,5249,5251],{"className":5250},[649],[574,5252,5254],{"className":5253,"style":1165},[653],[574,5255,5256,5259],{"style":1186},[574,5257],{"className":5258,"style":662},[661],[574,5260,5262],{"className":5261},[666,667,668,669],[574,5263,1012],{"className":5264},[631,635,669]," das Vorzeichen: Für gerade ",[574,5267,5269,5282],{"className":5268},[577],[574,5270,5272],{"className":5271},[581],[583,5273,5274],{"xmlns":585},[587,5275,5276,5280],{},[590,5277,5278],{},[596,5279,1012],{},[610,5281,1012],{"encoding":612},[574,5283,5285],{"className":5284,"ariaHidden":618},[617],[574,5286,5288,5292],{"className":5287},[622],[574,5289],{"className":5290,"style":5291},[626],"height:0.4306em;",[574,5293,1012],{"className":5294},[631,635]," liegt ",[574,5297,5299,5322],{"className":5298},[577],[574,5300,5302],{"className":5301},[581],[583,5303,5304],{"xmlns":585},[587,5305,5306,5320],{},[590,5307,5308],{},[1564,5309,5310,5316],{},[1091,5311,5312,5314],{},[596,5313,1560],{"mathvariant":1559},[596,5315,1012],{},[1573,5317,5318],{},[600,5319,841],{},[610,5321,3047],{"encoding":612},[574,5323,5325],{"className":5324,"ariaHidden":618},[617],[574,5326,5328,5331],{"className":5327},[622],[574,5329],{"className":5330,"style":3057},[626],[574,5332,5334,5337,5466],{"className":5333},[631],[574,5335],{"className":5336},[1654,1655],[574,5338,5340],{"className":5339},[1564],[574,5341,5343,5458],{"className":5342},[644,645],[574,5344,5346,5455],{"className":5345},[649],[574,5347,5349,5407,5415],{"className":5348,"style":3076},[653],[574,5350,5351,5354],{"style":2511},[574,5352],{"className":5353,"style":1675},[661],[574,5355,5357],{"className":5356},[666,667,668,669],[574,5358,5360],{"className":5359},[631,669],[574,5361,5363],{"className":5362},[631,1717,669],[574,5364,5366,5399],{"className":5365},[644,645],[574,5367,5369,5396],{"className":5368},[649],[574,5370,5372,5384],{"className":5371,"style":2533},[653],[574,5373,5375,5378],{"className":5374,"style":1732},[1731],[574,5376],{"className":5377,"style":1675},[661],[574,5379,5381],{"className":5380,"style":1739},[631,669],[574,5382,841],{"className":5383},[631,669],[574,5385,5386,5389],{"style":2548},[574,5387],{"className":5388,"style":1675},[661],[574,5390,5392],{"className":5391,"style":1753},[1752,669],[1755,5393,5394],{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},[1763,5395],{"d":1765},[574,5397,677],{"className":5398},[676],[574,5400,5402],{"className":5401},[649],[574,5403,5405],{"className":5404,"style":2568},[653],[574,5406],{},[574,5408,5409,5412],{"style":1684},[574,5410],{"className":5411,"style":1675},[661],[574,5413],{"className":5414,"style":1692},[1691],[574,5416,5417,5420],{"style":2581},[574,5418],{"className":5419,"style":1675},[661],[574,5421,5423],{"className":5422},[666,667,668,669],[574,5424,5426],{"className":5425},[631,669],[574,5427,5429,5432],{"className":5428},[631,669],[574,5430,1560],{"className":5431},[631,669],[574,5433,5435],{"className":5434},[640],[574,5436,5438],{"className":5437},[644],[574,5439,5441],{"className":5440},[649],[574,5442,5444],{"className":5443,"style":3172},[653],[574,5445,5446,5449],{"style":3175},[574,5447],{"className":5448,"style":3179},[661],[574,5450,5452],{"className":5451},[666,3183,3184,669],[574,5453,1012],{"className":5454},[631,635,669],[574,5456,677],{"className":5457},[676],[574,5459,5461],{"className":5460},[649],[574,5462,5464],{"className":5463,"style":2603},[653],[574,5465],{},[574,5467],{"className":5468},[1793,1655]," etwas über ",[574,5471,5473,5490],{"className":5472},[577],[574,5474,5476],{"className":5475},[581],[583,5477,5478],{"xmlns":585},[587,5479,5480,5488],{},[590,5481,5482],{},[593,5483,5484,5486],{},[596,5485,598],{},[596,5487,1012],{},[610,5489,1015],{"encoding":612},[574,5491,5493],{"className":5492,"ariaHidden":618},[617],[574,5494,5496,5499],{"className":5495},[622],[574,5497],{"className":5498,"style":627},[626],[574,5500,5502,5505],{"className":5501},[631],[574,5503,598],{"className":5504,"style":636},[631,635],[574,5506,5508],{"className":5507},[640],[574,5509,5511,5531],{"className":5510},[644,645],[574,5512,5514,5528],{"className":5513},[649],[574,5515,5517],{"className":5516,"style":1043},[653],[574,5518,5519,5522],{"style":657},[574,5520],{"className":5521,"style":662},[661],[574,5523,5525],{"className":5524},[666,667,668,669],[574,5526,1012],{"className":5527},[631,635,669],[574,5529,677],{"className":5530},[676],[574,5532,5534],{"className":5533},[649],[574,5535,5537],{"className":5536,"style":684},[653],[574,5538],{},", für ungerade etwas darunter.",{"title":5541,"searchDepth":5542,"depth":5542,"links":5543},"",2,[5544,5545,5546],{"id":562,"depth":5542,"text":563},{"id":3443,"depth":5542,"text":3444},{"id":4645,"depth":5542,"text":4646},[5548,5551,5554,5556,5558,5560,5562,5564,5567,5570,5573,5576],{"lhs":5549,"rhs":5550},"((1 + sqrt(5))\u002F2)^2","(1 + sqrt(5))\u002F2 + 1",{"lhs":5552,"rhs":5553},"((1 - sqrt(5))\u002F2)^2","(1 - sqrt(5))\u002F2 + 1",{"lhs":5555,"rhs":602},"(((1 + sqrt(5))\u002F2)^0 - ((1 - sqrt(5))\u002F2)^0)\u002Fsqrt(5)",{"lhs":5557,"rhs":728},"(((1 + sqrt(5))\u002F2)^1 - ((1 - sqrt(5))\u002F2)^1)\u002Fsqrt(5)",{"lhs":5559,"rhs":866},"(((1 + sqrt(5))\u002F2)^10 - ((1 - sqrt(5))\u002F2)^10)\u002Fsqrt(5)",{"lhs":5561,"rhs":4153},"(((1 + sqrt(5))\u002F2)^20 - ((1 - sqrt(5))\u002F2)^20)\u002Fsqrt(5)",{"lhs":5563,"rhs":4153},"round(((1 + sqrt(5))\u002F2)^20\u002Fsqrt(5))",{"lhs":5565,"rhs":5566},"round(((1 + sqrt(5))\u002F2)^20\u002Fsqrt(5) - 6765, 5)","0.00003",{"lhs":5568,"rhs":5569},"round((1 + sqrt(5))\u002F2, 3)","1.618",{"lhs":5571,"rhs":5572},"round((1 - sqrt(5))\u002F2, 3)","-0.618",{"lhs":5574,"rhs":5575},"round(89\u002F55, 4)","1.6182",{"lhs":5577,"rhs":5569},"round((1 + sqrt(5))\u002F2, 4)","n \\in \\mathbb{N}_0,\\ F_0 = 0,\\ F_1 = 1,\\ F_{n+1} = F_n + F_{n-1}","\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>\u003Cmsub>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N}_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\">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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">N\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\">0\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>\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>F\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F_0 = 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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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\">0\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:0.8389em;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>F\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F_1 = 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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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>\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\">1\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>F\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F_{n+1} = F_n + F_{n-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:0.8917em;vertical-align:-0.2083em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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 mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\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:0.2083em;\">\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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\">n\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:0.2222em;\">\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:0.8917em;vertical-align:-0.2083em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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 mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\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:0.2083em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fibonacci-binet","F_n = \\frac{1}{\\sqrt{5}} \\left( \\left(\\frac{1+\\sqrt{5}}{2}\\right)^{n} - \\left(\\frac{1-\\sqrt{5}}{2}\\right)^{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>\u003Cmsub>\u003Cmi>F\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmsqrt>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmsqrt>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmsqrt>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F_n = \\frac{1}{\\sqrt{5}} \\left( \\left(\\frac{1+\\sqrt{5}}{2}\\right)^{n} - \\left(\\frac{1-\\sqrt{5}}{2}\\right)^{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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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:-0.1389em;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\">n\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:3.0543em;vertical-align:-1.25em;\">\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:-2.2028em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9072em;\">\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\">5\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.8672em;\">\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:0.1328em;\">\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\">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:0.93em;\">\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 size4\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size4\">(\u003C\u002Fspan>\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:1.5842em;\">\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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan 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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=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size4\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.8043em;\">\u003Cspan style=\"top:-4.2029em;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 mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan 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size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\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":1012,"meaning":5607,"symbolHtml":5608},"Index, natürliche Zahl einschließlich 0","\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":5610,"meaning":5611,"symbolHtml":5612},"\\tfrac{1+\\sqrt{5}}{2}","goldener Schnitt Φ ≈ 1,618","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmfrac>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmsqrt>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmstyle>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\tfrac{1+\\sqrt{5}}{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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