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缩放黄金矩形（无限循环）

缩放黄金矩形（无限循环）
几何画板及绘图内容加载中，请稍等……
2017-06-21 05:52
多边形微积分极限几何作图滑块动画
①本范例演示通过连续缩放黄金矩形，观察其无限循环的几何现象；②涉及核心数学概念包括黄金分割、连续性、对数函数和相似变换；③作图要点——使用了Polygon（多边形）、Segment（线段）、Intersect（交点）等GeoGebra命令，构建并迭代生成嵌套的黄金矩形；④适合高中及以上数学学习者，用于理解连续性与几何变换的直观表现。

GeoGebra 命令及参数

  1. Polygon(C, O, 4) → poly1, f, g, h, i, D, E
  2. Segment(C, A) → j
  3. Segment(B, D) → k
  4. Polygon(B, E, 4) → poly2, l, m, n, q, F, G
  5. Intersect(k, n) → H
  6. Polygon(G, H, 4) → poly3, r, s, t, a, I, J
  7. Intersect(j, s) → K
  8. Polygon(I, K, 4) → poly4, b, c, d, e, L, M
  9. Polygon(F, L, 4) → poly5, f_1, g_1, h_1, i_1, N, P
  10. Polygon(H, P, 4) → poly6, j_1, k_1, l_1, m_1, Q, R
  11. Polygon(K, R, 4) → poly7, n_1, p_1, q_1, r_1, S, T
  12. Polygon(N, T, 4) → poly8, s_1, t_1, a_1, b_1, U, V
  13. Polygon(Q, V, 4) → poly9, c_1, d_1, e_1, f_2, W, Z
  14. Polygon(S, Z, 4) → poly10, g_2, h_2, i_2, j_2, A_1, B_1
  15. Polygon(U, B_1, 4) → poly11, k_2, l_2, m_2, n_2, C_1, D_1
  16. Polygon(W, D_1, 4) → poly12, p_2, q_2, r_2, s_2, E_1, F_1
  17. Polygon(A_1, F_1, 4) → poly13, t_2, a_2, b_2, c_2, G_1, H_1
  18. Polygon(C_1, H_1, 4) → poly14, d_2, e_2, f_3, g_3, I_1, J_1
  19. Polygon(E_1, J_1, 4) → poly15, h_3, i_3, j_3, k_3, K_1, L_1
  20. Polygon(G_1, L_1, 4) → poly16, l_3, m_3, n_3, p_3, M_1, N_1
  21. Polygon(I_1, N_1, 4) → poly17, q_3, r_3, s_3, t_3, O_1, P_1
  22. Polygon(K_1, P_1, 4) → poly18, a_3, b_3, c_3, d_3, Q_1, R_1
  23. Polygon(M_1, R_1, 4) → poly19, e_3, f_4, g_4, h_4, S_1, T_1
  24. Polygon(O_1, T_1, 4) → poly20, i_4, j_4, k_4, l_4, U_1, V_1
  25. Polygon(Q_1, V_1, 4) → poly21, m_4, n_4, p_4, q_4, W_1, Z_1
  26. Intersect(j, k) → Z0