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正方形循环图形探索

正方形循环图形探索
几何画板及绘图内容加载中，请稍等……
2014-07-14 22:49
圆多边形几何作图函数图像
①本范例演示通过正方形循环拼接探索多边形铺砖的规律；②涉及核心数学概念包括多边形、正方形、外接圆、菱形、条形图与直方图、等边三角形；③作图要点运用了Polygon（多边形）、Intersect（交点）、Point（点）、Rotate（旋转）等GeoGebra命令与对象；④适合初中及以上学生用于几何图形探索与数据分析教学。

GeoGebra 命令及参数

  1. Polygon(A_1, B_1, 4) → poly1_1, a_1, b_1, c_1, d_1, C_1, D_1
  2. Intersect(c_1, d_1) → E_1
  3. Intersect(b_1, c_1) → F_1
  4. Intersect(a_1, b_1) → G_1
  5. Intersect(a_1, d_1) → H_1
  6. Point(Circle[A, a_1]) → B
  7. Rotate(B + (b_1, 0), Angle[C_1 - B_1] + Angle[B - A] - Angle[B_1 - A_1], B) → C
  8. Rotate(C + (c_1, 0), Angle[D_1 - C_1] + Angle[C - B] - Angle[C_1 - B_1], C) → D
  9. Polygon(A, B, C, D) → poly1, a, b, c, d
  10. Point(Circle[E, a_1]) → F
  11. Rotate(F + (b_1, 0), Angle[C_1 - B_1] + Angle[F - E] - Angle[B_1 - A_1], F) → G
  12. Rotate(G + (c_1, 0), Angle[D_1 - C_1] + Angle[G - F] - Angle[C_1 - B_1], G) → H
  13. Polygon(E, F, G, H) → poly2, e, f, g, h
  14. Point(Circle[I, a_1]) → J
  15. Rotate(J + (b_1, 0), Angle[C_1 - B_1] + Angle[J - I] - Angle[B_1 - A_1], J) → K
  16. Rotate(K + (c_1, 0), Angle[D_1 - C_1] + Angle[K - J] - Angle[C_1 - B_1], K) → L
  17. Polygon(I, J, K, L) → poly3, i, j, k, l
  18. Point(Circle[M, a_1]) → N
  19. Rotate(N + (b_1, 0), Angle[C_1 - B_1] + Angle[N - M] - Angle[B_1 - A_1], N) → O
  20. Rotate(O + (c_1, 0), Angle[D_1 - C_1] + Angle[O - N] - Angle[C_1 - B_1], O) → P
  21. Polygon(M, N, O, P) → poly4, m, n, o, p
  22. Point(Circle[Q, a_1]) → R
  23. Rotate(R + (b_1, 0), Angle[C_1 - B_1] + Angle[R - Q] - Angle[B_1 - A_1], R) → S
  24. Rotate(S + (c_1, 0), Angle[D_1 - C_1] + Angle[S - R] - Angle[C_1 - B_1], S) → T
  25. Polygon(Q, R, S, T) → poly5, q, r, s, t
  26. Point(Circle[U, a_1]) → V
  27. Rotate(V + (b_1, 0), Angle[C_1 - B_1] + Angle[V - U] - Angle[B_1 - A_1], V) → W
  28. Rotate(W + (c_1, 0), Angle[D_1 - C_1] + Angle[W - V] - Angle[C_1 - B_1], W) → Z
  29. Polygon(U, V, W, Z) → poly6, u, v, w, z
  30. Point(Circle[I_1, a_1]) → J_1
  31. Rotate(J_1 + (b_1, 0), Angle[C_1 - B_1] + Angle[J_1 - I_1] - Angle[B_1 - A_1], J_1) → K_1
  32. Rotate(K_1 + (c_1, 0), Angle[D_1 - C_1] + Angle[K_1 - J_1] - Angle[C_1 - B_1], K_1) → L_1
  33. Polygon(I_1, J_1, K_1, L_1) → poly7, i_1, j_1, k_1, l_1
  34. Point(Circle[M_1, a_1]) → N_1
  35. Rotate(N_1 + (b_1, 0), Angle[C_1 - B_1] + Angle[N_1 - M_1] - Angle[B_1 - A_1], N_1) → O_1
  36. Rotate(O_1 + (c_1, 0), Angle[D_1 - C_1] + Angle[O_1 - N_1] - Angle[C_1 - B_1], O_1) → P_1
  37. Polygon(M_1, N_1, O_1, P_1) → poly8, m_1, n_1, o_1, p_1
  38. Point(Circle[Q_1, a_1]) → R_1
  39. Rotate(R_1 + (b_1, 0), Angle[C_1 - B_1] + Angle[R_1 - Q_1] - Angle[B_1 - A_1], R_1) → S_1
  40. Rotate(S_1 + (c_1, 0), Angle[D_1 - C_1] + Angle[S_1 - R_1] - Angle[C_1 - B_1], S_1) → T_1
  41. Polygon(Q_1, R_1, S_1, T_1) → poly9, q_1, r_1, s_1, t_1
  42. Point(Circle[U_1, a_1]) → V_1
  43. Rotate(V_1 + (b_1, 0), Angle[C_1 - B_1] + Angle[V_1 - U_1] - Angle[B_1 - A_1], V_1) → W_1
  44. Rotate(W_1 + (c_1, 0), Angle[D_1 - C_1] + Angle[W_1 - V_1] - Angle[C_1 - B_1], W_1) → Z_1
  45. Polygon(U_1, V_1, W_1, Z_1) → poly10, u_1, v_1, w_1, z_1
  46. Point(Circle[B_2, a_1]) → C_2
  47. Rotate(C_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[C_2 - B_2] - Angle[B_1 - A_1], C_2) → D_2
  48. Rotate(D_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[D_2 - C_2] - Angle[C_1 - B_1], D_2) → E_2
  49. Polygon(B_2, C_2, D_2, E_2) → poly11, b_2, c_2, d_2, e_2
  50. Point(Circle[F_2, a_1]) → G_2
  51. Rotate(G_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[G_2 - F_2] - Angle[B_1 - A_1], G_2) → H_2
  52. Rotate(H_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[H_2 - G_2] - Angle[C_1 - B_1], H_2) → I_2
  53. Polygon(F_2, G_2, H_2, I_2) → poly12, f_2, g_2, h_2, i_2
  54. Point(Circle[J_2, a_1]) → K_2
  55. Rotate(K_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[K_2 - J_2] - Angle[B_1 - A_1], K_2) → L_2
  56. Rotate(L_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[L_2 - K_2] - Angle[C_1 - B_1], L_2) → M_2
  57. Polygon(J_2, K_2, L_2, M_2) → poly13, j_2, k_2, l_2, m_2
  58. Point(Circle[N_2, a_1]) → O_2
  59. Rotate(O_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[O_2 - N_2] - Angle[B_1 - A_1], O_2) → P_2
  60. Rotate(P_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[P_2 - O_2] - Angle[C_1 - B_1], P_2) → Q_2
  61. Polygon(N_2, O_2, P_2, Q_2) → poly14, n_2, o_2, p_2, q_2
  62. Point(Circle[R_2, a_1]) → S_2
  63. Rotate(S_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[S_2 - R_2] - Angle[B_1 - A_1], S_2) → T_2
  64. Rotate(T_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[T_2 - S_2] - Angle[C_1 - B_1], T_2) → U_2
  65. Polygon(R_2, S_2, T_2, U_2) → poly15, r_2, s_2, t_2, u_2
  66. Point(Circle[V_2, a_1]) → W_2
  67. Rotate(W_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[W_2 - V_2] - Angle[B_1 - A_1], W_2) → Z_2
  68. Rotate(Z_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[Z_2 - W_2] - Angle[C_1 - B_1], Z_2) → A_3
  69. Polygon(V_2, W_2, Z_2, A_3) → poly16, v_2, w_2, z_2, a_3
  70. Point(Circle[B_3, a_1]) → C_3
  71. Rotate(C_3 + (b_1, 0), Angle[C_1 - B_1] + Angle[C_3 - B_3] - Angle[B_1 - A_1], C_3) → D_3
  72. Rotate(D_3 + (c_1, 0), Angle[D_1 - C_1] + Angle[D_3 - C_3] - Angle[C_1 - B_1], D_3) → E_3
  73. Polygon(B_3, C_3, D_3, E_3) → poly17, b_3, c_3, d_3, e_3
  74. Point(Circle[F_3, a_1]) → G_3
  75. Rotate(G_3 + (b_1, 0), Angle[C_1 - B_1] + Angle[G_3 - F_3] - Angle[B_1 - A_1], G_3) → H_3
  76. Rotate(H_3 + (c_1, 0), Angle[D_1 - C_1] + Angle[H_3 - G_3] - Angle[C_1 - B_1], H_3) → I_3
  77. Polygon(F_3, G_3, H_3, I_3) → poly18, f_3, g_3, h_3, i_3
  78. Point(Circle[J_3, a_1]) → K_3
  79. Rotate(K_3 + (b_1, 0), Angle[C_1 - B_1] + Angle[K_3 - J_3] - Angle[B_1 - A_1], K_3) → L_3
  80. Rotate(L_3 + (c_1, 0), Angle[D_1 - C_1] + Angle[L_3 - K_3] - Angle[C_1 - B_1], L_3) → M_3
  81. Polygon(J_3, K_3, L_3, M_3) → poly19, j_3, k_3, l_3, m_3

AI 绘图提示语参考

绘制一个由多个正方形组成的图案，每个正方形通过旋转和相交的方式连接。首先创建一个正方形，然后在其基础上通过旋转和相交生成多个新的正方形，每个新正方形都与前一个正方形相邻。使用圆形来辅助旋转和定位，最终形成一个复杂的正方形环状图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。