黄金矩形 by Jonathan Garfield

黄金矩形 by Jonathan Garfield
几何画板及绘图内容加载中,请稍等……
2015-02-03 22:42
这个范例展示了黄金矩形的构造。黄金矩形是一种特殊的矩形,其长宽比为黄金比例。本例涉及的核心数学概念包括比例与相似。通过使用GeoGebra命令如Polygon, Midpoint, Circle等,可以动态地构造黄金矩形。适合初中及以上学生学习比例与黄金分割的概念。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Midpoint(A, B) → E
  3. Circle(E, C) → e
  4. Ray(A, B) → f
  5. Intersect(e, f, 1) → F
  6. Ray(D, C) → g
  7. OrthogonalLine(F, f) → h
  8. Intersect(h, g) → G
  9. Segment(C, G) → i
  10. Segment(G, F) → j
  11. Segment(F, B) → k
  12. Polygon(G, C, 4) → poly2, l, m, n, p, H, I
  13. Polygon(F, I, 4) → poly3, q, r, s, t, J, K
  14. Polygon(B, K, 4) → poly4, a_1, b_1, c_1, d_1, L, M
  15. Polygon(H, M, 4) → poly5, e_1, f_1, g_1, h_1, N, O
  16. Polygon(J, O, 4) → poly6, i_1, j_1, k_1, l_1, P, Q
  17. Polygon(L, Q, 4) → poly7, m_1, n_1, p_1, q_1, R, S
  18. Polygon(N, S, 4) → poly8, r_1, s_1, t_1, a_2, T, U
  19. Polygon(P, U, 4) → poly9, b_2, c_2, d_2, e_2, V, W
  20. Polygon(R, W, 4) → poly10, f_2, g_2, h_2, i_2, Z, A_1
  21. Polygon(T, A_1, 4) → poly11, j_2, k_2, l_2, m_2, B_1, C_1
  22. Polygon(V, C_1, 4) → poly12, n_2, p_2, q_2, r_2, D_1, E_1
  23. Polygon(Z, E_1, 4) → poly13, s_2, t_2, a_3, b_3, F_1, G_1
  24. Polygon(B_1, G_1, 4) → poly14, c_3, d_3, e_3, f_3, H_1, I_1
  25. Polygon(D_1, I_1, 4) → poly15, g_3, h_3, i_3, j_3, J_1, K_1
  26. Polygon(F_1, K_1, 4) → poly16, k_3, l_3, m_3, n_3, L_1, M_1
  27. Polygon(H_1, M_1, 4) → poly17, p_3, q_3, r_3, s_3, N_1, O_1
  28. CircleArc(N_1, O_1, M_1) → t_3
  29. CircleArc(L_1, M_1, K_1) → c_4
  30. CircleArc(J_1, K_1, I_1) → d_4
  31. CircleArc(H_1, I_1, G_1) → e_4
  32. CircleArc(F_1, G_1, E_1) → f_4
  33. CircleArc(D_1, E_1, C_1) → g_4
  34. CircleArc(B_1, C_1, A_1) → h_4
  35. CircleArc(Z, A_1, W) → k_4
  36. CircleArc(V, W, U) → p_4
  37. CircleArc(T, U, S) → q_4
  38. CircleArc(R, S, Q) → r_4
  39. CircleArc(P, Q, O) → s_4
  40. CircleArc(N, O, M) → t_4
  41. CircleArc(L, M, K) → c_5
  42. CircleArc(J, K, I) → d_5
  43. CircleArc(H, I, C) → e_5
  44. CircleArc(B, C, A) → f_5

AI 绘图提示语参考

绘制一个黄金矩形,首先创建一个矩形ABCD,然后找到AB的中点E,以E为圆心,C为半径画圆,交AB延长线于F,再作FC的垂线交DC延长线于G,连接CG、GF、FB,形成新的矩形CGFB,重复此过程,每次以新矩形的对角线为直径画圆,交相邻边的延长线于新点,连接这些点形成新的矩形,直到图形变得足够小为止。
以上提示语为根据原始绘图命令整理而来,仅供参考。