图案块对称性

图案块对称性
几何画板及绘图内容加载中,请稍等……
2017-09-22 02:58
所属专题 Symmetry Explorations
①本范例演示如何基于给定图案创建对称图形;②涉及核心数学概念包括对称性、变异性、全等性、外接圆、立方体、坐标几何;③作图要点:使用 GeoGebra 命令如点、线段、多边形、旋转、角度、圆、交点、中点等;④适合初中及以上学生学习和探索几何对称性。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 6) → poly1, g, F, h, i, j, k, l, C, D, E
  4. Point(Circle[G, a]) → H
  5. Segment(G, H) → m
  6. Polygon(G, H, 3) → poly2, n, p, q, I
  7. Point(Circle[J, a]) → K
  8. Segment(J, K) → r
  9. Polygon(J, K, 3) → poly3, s, t, b, L
  10. Polygon(L, K, 3) → poly4, c, d, e, M
  11. Polygon(J, K, M, L) → poly5, j_1, k_1, m_1, l_1
  12. Point(Circle[S, a]) → T
  13. Segment(S, T) → a_1
  14. Polygon(S, T, 4) → poly10, b_1, c_1, d_1, e_1, U, V
  15. Point(Circle[W, a]) → Z
  16. Segment(W, Z) → f_2
  17. Rotate(Z, 30°, W) → Z'
  18. Angle(Z, W, Z') → α
  19. Circle(Z, W) → c_2
  20. Circle(Z', W) → d_2
  21. Intersect(c_2, d_2, 2) → A_1
  22. Polygon(W, Z, A_1, Z') → poly11, w, z_1, a_2, z'
  23. Point(Circle[A_2, a]) → B_1
  24. Segment(A_2, B_1) → f_3
  25. Polygon(A_2, B_1, 6) → poly1_1, g_2, F_1, h_2, i_2, j_2, k_2, l_2, C_1, D_1, E_1
  26. Point(Circle[W_1, a]) → Z_1
  27. Segment(W_1, Z_1) → f_4
  28. Rotate(Z_1, 30°, W_1) → Z'_1
  29. Angle(Z_1, W_1, Z'_1) → α_1
  30. Circle(Z_1, W_1) → c_3
  31. Circle(Z'_1, W_1) → d_3
  32. Intersect(c_3, d_3, 2) → A_3
  33. Point(Circle[W_2, a]) → Z_2
  34. Segment(W_2, Z_2) → f_5
  35. Rotate(Z_2, 30°, W_2) → Z'_2
  36. Angle(Z_2, W_2, Z'_2) → α_2
  37. Circle(Z_2, W_2) → c_4
  38. Circle(Z'_2, W_2) → d_4
  39. Intersect(c_4, d_4, 2) → A_4
  40. Polygon(W_2, Z_2, A_4, Z'_2) → poly11_1, w_1, z_2, a_3, z'_1
  41. Point(Circle[G_1, (2 * a)]) → H_1
  42. Segment(G_1, H_1) → m_2
  43. Polygon(G_1, H_1, 3) → poly12, s_2, t_2, b_2, I_1
  44. Midpoint(G_1, I_1) → J_1
  45. Midpoint(H_1, I_1) → K_1
  46. Polygon(G_1, H_1, K_1, J_1) → poly13, g_3, h_3, k_3, j_3
  47. Point(Circle[G_2, (2 * a)]) → H_2
  48. Segment(G_2, H_2) → m_3
  49. Polygon(G_2, H_2, 3) → poly12_1, s_3, t_3, b_3, I_2
  50. Midpoint(G_2, I_2) → J_2
  51. Midpoint(H_2, I_2) → K_2
  52. Polygon(G_2, H_2, K_2, J_2) → poly13_1, g_4, h_4, k_4, j_4
  53. Point(Circle[G_3, a]) → H_3
  54. Segment(G_3, H_3) → m_4
  55. Polygon(G_3, H_3, 3) → poly2_1, n_1, p_1, q_1, I_3
  56. Point(Circle[J_3, a]) → K_3
  57. Segment(J_3, K_3) → r_1
  58. Polygon(J_3, K_3, 3) → poly3_1, s_1, t_1, b_4, L_1
  59. Polygon(L_1, K_3, 3) → poly4_1, c_5, d_5, e_2, M_1
  60. Polygon(J_3, K_3, M_1, L_1) → poly5_1, j_5, k_5, m_5, l_3
  61. Point(Circle[W_3, a]) → Z_3
  62. Segment(W_3, Z_3) → f_1
  63. Rotate(Z_3, 30°, W_3) → Z'_3
  64. Angle(Z_3, W_3, Z'_3) → α_3
  65. Circle(Z_3, W_3) → c_6
  66. Circle(Z'_3, W_3) → d_6
  67. Intersect(c_6, d_6, 2) → A_5
  68. Polygon(W_3, Z_3, A_5, Z'_3) → poly11_2, w_2, z_3, a_4, z'_2
  69. Point(Circle[G_4, (2 * a)]) → H_4
  70. Segment(G_4, H_4) → m_6
  71. Polygon(G_4, H_4, 3) → poly12_2, s_4, t_4, b_5, I_4
  72. Midpoint(G_4, I_4) → J_4
  73. Midpoint(H_4, I_4) → K_4
  74. Polygon(G_4, H_4, K_4, J_4) → poly13_2, g_1, h_1, k_6, j_6
  75. Point(Circle[J_5, a]) → K_5
  76. Segment(J_5, K_5) → r_2
  77. Polygon(J_5, K_5, 3) → poly3_2, s_5, t_5, b_6, L_2
  78. Polygon(L_2, K_5, 3) → poly4_2, c_7, d_7, e_3, M_2
  79. Polygon(J_5, K_5, M_2, L_2) → poly5_2, j_7, k_7, m_7, l_4

AI 绘图提示语参考

绘制一个由多个对称几何图形组成的图案。首先,以一个大圆上的点为起点,构造一个正六边形;接着,在六边形的一侧构造一个正三角形,并在其相邻位置再构造两个正三角形,其中一个与另一个共用一条边,形成菱形组合。然后,构造一个正方形,以及一个由两个相交圆和旋转点形成的菱形。重复这些基本形状,包括另一个正六边形、两个菱形和一个更大的正三角形,并在大三角形内部通过中点连接构造一个四边形。所有图形围绕中心对称分布,整体呈现对称美感。
以上提示语为根据原始绘图命令整理而来,仅供参考。