动画演示抛物线与矩形和
几何画板及绘图内容加载中,请稍等……
①这个范例通过动画演示抛物线与矩形和的关系,展示了上和与下和如何逼近抛物线下的面积;②涉及的核心数学概念包括抛物线、一般四边形、上和与下和(黎曼和)、相关性、随机变量和有理数;③作图要点使用了Line, Parabola, Point, OrthogonalLine, Intersect, Dilate, Segment, Angle, Rotate, Circle, Ray等GeoGebra命令和对象;④适合高中数学教学,用于理解黎曼积分的概念。
GeoGebra 命令及参数
Line(A, B) → aParabola(C, a) → cPoint(c) → DOrthogonalLine(D, a) → bIntersect(a, b) → EDilate(C, If[0 < d ≤ 1, 1 - d, 0], D) → C'Segment(C, C') → eDilate(D, If[1 < d ≤ 2, 2 - d, 0], E) → D'Segment(D, D') → fAngle(A, E, D) → αAngle(E, D, C) → βRotate(C, If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C'_1Rotate(C', If[2 < d ≤ 3, ((-(d - 2)) * β), (-β)], D) → C''Segment(C'_1, C'') → e'OrthogonalLine(C, a) → gIntersect(c, g) → V, SOrthogonalLine(C, g) → hIntersect(c, h) → G, HCircle(C, 2) → kIntersect(k, c, 1) → IIntersect(k, c, 1) → JIntersect(k, g) → K, LSegment(V, C) → iCircle(G, i) → pIntersect(p, h) → F, MCircle(H, i) → qIntersect(q, h) → N, ORay(C, L) → jAngle(M, C, L) → γDilate(V, If[3 < d ≤ 4, 4 - d, 0], C) → V'Segment(V, V') → lDilate(G, If[5 < d ≤ 6, 6 - d, 0], M) → G'Segment(G, G') → mDilate(M, If[6 < d ≤ 7, 7 - d, 0], C) → M'Segment(M, M') → nDilate(C, If[7 < d ≤ 8, 8 - d, 0], N) → C'_2Segment(C, C'_2) → rDilate(N, If[8 < d ≤ 9, 9 - d, 0], H) → N'Segment(N, N') → sRotate(V, If[9 < d ≤ 10, ((d - 9) * π / 2), π / 2], C) → V'_1Rotate(V', If[9 < d ≤ 10, ((d - 9) * π / 2), π / 2], C) → V''Segment(V'_1, V'') → l'Rotate(V, If[9 < d ≤ 10, ((-(d - 9)) * π / 2), ((-π)) / 2], C) → V'_2Rotate(V', If[9 < d ≤ 10, ((-(d - 9)) * π / 2), ((-π)) / 2], C) → V''_1Segment(V'_2, V''_1) → l'_1Rotate(V'_1, If[10 < d ≤ 11, ((d - 10) * π), π], M) → PRotate(V'', If[10 < d ≤ 11, ((d - 10) * π), π], M) → V'''Segment(P, V''') → l''Rotate(V'_2, If[10 < d ≤ 11, ((d - 10) * π), π], N) → QRotate(V''_1, If[10 < d ≤ 11, ((d - 10) * π), π], N) → RSegment(Q, R) → t
AI 绘图提示语参考
绘制一个抛物线,并围绕它展示上、下矩形求和逼近抛物线下方面积的过程。首先画一条直线AB,然后以C点为顶点画抛物线c。接着在抛物线上取点D,作D点关于直线AB的垂线b,找到两线交点E。通过D点对C点进行缩放变换,生成C'点,连接C和C'。继续进行一系列旋转、缩放和交点操作,逐步构建多个矩形,展示上、下求和逼近过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。