Gal 3: 圆链几何演示
几何画板及绘图内容加载中,请稍等……
①本范例演示了通过动态圆链构建复杂几何图形的现象;②涉及的核心数学概念包括圆、几何作图、不等式、向量与三维空间;③作图要点提炼自构造摘要,使用了Point(点)、Segment(线段)、Circle(圆)、Intersect(交点)、CircleSector(圆扇形)等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解空间几何与参数化作图的原理与技巧。
GeoGebra 命令及参数
Point(yAxis) → A_0Point(Circle[A_0, (2 * r)]) → A_1Segment(A_0, A_1) → fPoint(Circle[A_1, (2 * r)]) → A_2Segment(A_1, A_2) → gPoint(Circle[A_2, (2 * r)]) → A_3Segment(A_2, A_3) → hPoint(Circle[A_3, (2 * r)]) → A_4Segment(A_3, A_4) → iPoint(Circle[A_4, (2 * r)]) → A_5Segment(A_4, A_5) → jPoint(Circle[A_5, (2 * r)]) → A_6Segment(A_5, A_6) → kPoint(Circle[A_6, (2 * r)]) → A_7Segment(A_6, A_7) → lPoint(Circle[A_7, (2 * r)]) → A_8Segment(A_7, A_8) → mPoint(Circle[A_8, (2 * r)]) → A_9Segment(A_8, A_9) → nPoint(Circle[A_9, (2 * r)]) → A_{10}Segment(A_9, A_{10}) → pPoint(Circle[A_{10}, (2 * r)]) → A_{11}Segment(A_{10}, A_{11}) → qPoint(Circle[A_{11}, (2 * r)]) → A_{12}Segment(A_{11}, A_{12}) → sPoint(Circle[A_{12}, (2 * r)]) → A_{13}Segment(A_{12}, A_{13}) → tPoint(Circle[A_{13}, (2 * r)]) → A_{14}Segment(A_{13}, A_{14}) → aCircle(A_0, (2 * r)) → dCircle(A_{14}, (2 * r)) → eIntersect(d, e) → B, A_{15}, ,Segment(A_{15}, A_{14}) → bSegment(A_{15}, A_0) → cCircle(A_0, r) → c_1Circle(A_1, r) → d_1Circle(A_2, r) → e_1Circle(A_3, r) → f_1Circle(A_4, r) → g_1Circle(A_5, r) → h_1Circle(A_6, r) → k_1Circle(A_7, r) → p_1Circle(A_8, r) → q_1Circle(A_9, r) → r_1Circle(A_{11}, r) → s_1Circle(A_{10}, r) → t_1Circle(A_{12}, r) → c_2Circle(A_{13}, r) → d_2Circle(A_{14}, r) → e_2Circle(A_{15}, r) → f_2Intersect(e_1, g) → A,Intersect(d_1, f) → C,Intersect(c_1, c) → D,Intersect(f_2, b) → E,Intersect(e_2, a) → F,Intersect(d_2, t) → G,Intersect(c_2, s) → H,Intersect(s_1, q) → I,Intersect(t_1, p) → J,Intersect(r_1, n) → K,Intersect(q_1, m) → L,Intersect(p_1, l) → M,Intersect(k_1, k) → N,Intersect(h_1, j) → O,Intersect(f_1, i) → P,Intersect(f_1, h) → Q,CircleSector(A_0, C, D) → g_2CircleSector(A_1, A, C) → h_2CircleSector(A_2, Q, A) → k_2CircleSector(A_3, P, Q) → p_2CircleSector(A_4, O, P) → q_2CircleSector(A_5, N, O) → r_2CircleSector(A_6, M, N) → s_2CircleSector(A_7, L, M) → t_2CircleSector(A_8, K, L) → c_3CircleSector(A_9, J, K) → d_3CircleSector(A_{10}, I, J) → e_3CircleSector(A_{11}, H, I) → f_3CircleSector(A_{12}, G, H) → g_3CircleSector(A_{13}, F, G) → h_3CircleSector(A_{14}, E, F) → k_3CircleSector(A_{15}, D, E) → p_3
AI 绘图提示语参考
在三维空间中,从y轴上的一个点开始,依次以该点为圆心、以两倍半径作圆,并在每个圆上取一点作为下一个圆心,重复此过程,形成一条由十五个点组成的链。连接相邻点得到一系列线段,构成一条折线。首尾两个点分别以两倍半径作圆,两圆相交于两个点,取其中一个点与首尾点相连,形成闭合三角形。再以每个链上的点为圆心、以单倍半径作小圆,形成一串相切的小圆链,整体呈现几何构造的链条与闭合结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。