动态几何图形演示 by Tim Brzezinski (5)
几何画板及绘图内容加载中,请稍等……
①本范例动态演示了圆、菱形、角度等几何图形的相互关系与变换;②涉及核心数学概念包括圆、菱形、角度、变换、比例等;③作图要点提炼自构造摘要,使用了Circle, Distance, PointIn, Semicircle, Intersect, Line, Angle, Dilate, Midpoint, Segment, Rotate, Vector, CircleArc, Point, Ray, CircleSector, Translate等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解几何变换与概率统计中的正态分布关系。
GeoGebra 命令及参数
Circle(A, B) → cDistance(A, B) → aPointIn(b) → C_1Semicircle(A, C_1) → dSemicircle(C_1, A) → eIntersect(c, d, 1) → D_1Intersect(c, e, 1) → CLine(C_1, C) → fLine(C_1, D_1) → gLine(C, g) → hIntersect(c, h) → F, DLine(C_1, D) → iIntersect(c, i, 2) → ELine(C, E) → jIntersect(g, j) → GAngle(A, D_1, G) → αAngle(C_1, C, A) → βDilate(C_1, If[0 < k ≤ 1, 1 - k, 0], G) → HMidpoint(C, C_1) → IDilate(C_1, If[0 < k ≤ 1, 1 - k, 0], I) → JSegment(C_1, J) → lSegment(C_1, H) → mDilate(G, If[0 < k ≤ 1, 1 - k, 0], G) → G'Dilate(A, If[1 < k ≤ 2, 2 - k, 0], D_1) → A'Dilate(A, If[1 < k ≤ 2, 2 - k, 0], C) → A'_1Segment(A, A') → nSegment(A, A'_1) → pDilate(G, If[1 < k ≤ 2, 2 - k, 0], D_1) → G'_1Dilate(I, If[1 < k ≤ 2, 2 - k, 0], C) → I'Segment(G, G'_1) → qSegment(I, I') → rRotate(A, 90°, C) → A'_2Angle(A, C, A'_2) → γCircle(C_1, (0.4 * Distance[C_1, G])) → tAngle(G, C_1, C) → δIntersect(t, m) → L,Rotate(L, If[4 < k ≤ 5, ((k - 4) * δ), δ], C_1) → L'Dilate(C_1, If[5.5 < k ≤ 6.5, 6.5 - k, 0], C) → MVector(C_1, M) → uDilate(E, If[7 < k ≤ 8, 8 - k, 0], C_1) → E'Segment(E, E') → h_1Dilate(C, If[8.5 < k ≤ 9.5, 9.5 - k, 0], E) → C'_1Dilate(E, If[9.5 < k ≤ 10.5, 10.5 - k, 0], G) → E'_1Rotate(C_1, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → NRotate(G, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → G'_2CircleArc(A, D_1, C) → e_1Point(e_1) → OLine(O, C_1) → n_1Line(D_1, n_1) → p_1Intersect(e_1, p_1) → P, QLine(O, Q) → f_1Midpoint(O, Q) → KCircle(O, (0.5 * Distance[O, K])) → sIntersect(s, n_1) → R, SIntersect(s, f_1, 1) → TAngle(R, O, T) → εLine(C, Q) → g_1Intersect(n_1, g_1) → UIntersect(c, n_1) → V, WDilate(O, If[4 < k ≤ 5, 5 - k, 0], U) → O'Segment(O, O') → q_1Dilate(U, If[5 < k ≤ 6, 6 - k, 0], W) → U'Segment(U, U') → r_1Ray(O, R) → s_1Dilate(W, If[6 < k ≤ 7, 7 - k, 0], C_1) → W'Segment(W, W') → t_1Circle(Q, 3) → c_1Intersect(c_1, p_1, 1) → ZRay(Q, Z) → a_1Dilate(D_1, If[7 < k ≤ 8, 8 - k, 0], Q) → A_1Segment(D_1, A_1) → b_1Rotate(R, If[8.5 < k ≤ 9.5, ((k - 8.5) * ε), ε], O) → R'CircleSector(O, R, R') → d_1Dilate(O, If[10 < k ≤ 11, 11 - k, 0], Q) → O'_1Vector(O, O'_1) → vTranslate(d_1, v) → c_2Dilate(C, If[11 < k ≤ 12, 12 - k, 0], U) → C'Segment(C, C') → i_1Dilate(U, If[12 < k ≤ 13, 13 - k, 0], Q) → U'_1Segment(U, U'_1) → j_1Angle(O, U, A) → ζDilate(A, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → A'_3Segment(A, A'_3) → k_1Dilate(O, If[13.5 < k ≤ 14.5, 14.5 - k, 0], U) → O'_2Segment(O, O'_2) → l_1Rotate(O, If[15 < k ≤ 16, ((k - 15) * π), π], U) → O'_3Rotate(O'_2, If[15 < k ≤ 16, ((k - 15) * π), π], U) → B_1Segment(O'_3, B_1) → m_1Segment(O, O'_1) → f_2Circle(O, 1) → d_2Intersect(d_2, f_1, 1) → E_1Ray(O, E_1) → g_2
AI 绘图提示语参考
画一个动态几何图形,展示圆形、菱形和角之间的关系与变换。包含两个半圆相交形成交点,连接这些点形成菱形和直线。标记关键角,并展示菱形通过缩放和旋转与正态分布的关系。图形应动态变化,展示几何变换过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。