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旋转正方形的镶嵌

旋转正方形的镶嵌
几何画板及绘图内容加载中，请稍等……
2020-12-08 01:25
多边形几何作图
这个范例演示了通过旋转正方形生成的镶嵌图案。涉及的核心数学概念包括旋转、正方形和三角形。通过使用Polygon和Rotate命令，可以构造出一系列旋转的正方形，形成美丽的镶嵌图案。适合初中及以上学生学习几何变换和镶嵌图案。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Rotate(E, 90°, A) → E'
  3. Rotate(F, 90°, A) → F'
  4. Rotate(G, 90°, A) → G'
  5. Rotate(H, 90°, A) → H'
  6. Rotate(I, 90°, C) → I'
  7. Rotate(J, 90°, C) → J'
  8. Polygon(A, E, I, D, H', G', F', E', F, G, H, B, I', J', C, J) → poly2, a, j, i_1, d, h', g', f', e', e, f_1, g_1, h_1, b, i', j', c
  9. Rotate(A, (-(90°)), A) → A'
  10. Rotate(E, (-(90°)), A) → E'_{1}
  11. Rotate(F, (-(90°)), A) → F'_{1}
  12. Rotate(G, (-(90°)), A) → G'_{1}
  13. Rotate(H, (-(90°)), A) → H'_{1}
  14. Rotate(B, (-(90°)), A) → B'
  15. Rotate(I', (-(90°)), A) → I''
  16. Rotate(J', (-(90°)), A) → J''
  17. Rotate(C, (-(90°)), A) → C'
  18. Rotate(J, (-(90°)), A) → J'_{1}
  19. Rotate(I, (-(90°)), A) → I'_{1}
  20. Rotate(D, (-(90°)), A) → D'
  21. Rotate(H', (-(90°)), A) → H''
  22. Rotate(G', (-(90°)), A) → G''
  23. Rotate(F', (-(90°)), A) → F''
  24. Rotate(E', (-(90°)), A) → E''
  25. Polygon(A', E'_{1}, I'_{1}, D', H'', G'', F'', E'', F'_{1}, G'_{1}, H'_{1}, B', I'', J'', C', J'_{1}) → poly2', a', j'_{1}, i'_{1}, d', h'', g'', f'', e'', e'_{1}, f'_{1}, g'_{1}, h'_{1}, b', i'', j'', c'
  26. Rotate(A, 90°, A) → A'_{1}
  27. Rotate(E, 90°, A) → E'_{2}
  28. Rotate(F, 90°, A) → F'_{2}
  29. Rotate(G, 90°, A) → G'_{2}
  30. Rotate(H, 90°, A) → H'_{2}
  31. Rotate(B, 90°, A) → B'_{1}
  32. Rotate(I', 90°, A) → I''_{1}
  33. Rotate(J', 90°, A) → J''_{1}
  34. Rotate(C, 90°, A) → C'_{1}
  35. Rotate(J, 90°, A) → J'_{2}
  36. Rotate(I, 90°, A) → I'_{2}
  37. Rotate(D, 90°, A) → D'_{1}
  38. Rotate(H', 90°, A) → H''_{1}
  39. Rotate(G', 90°, A) → G''_{1}
  40. Rotate(F', 90°, A) → F''_{1}
  41. Rotate(E', 90°, A) → E''_{1}
  42. Polygon(A'_{1}, E'_{2}, I'_{2}, D'_{1}, H''_{1}, G''_{1}, F''_{1}, E''_{1}, F'_{2}, G'_{2}, H'_{2}, B'_{1}, I''_{1}, J''_{1}, C'_{1}, J'_{2}) → poly2'_{1}, a'_{1}, j'_{2}, i'_{2}, d'_{1}, h''_{1}, g''_{1}, f''_{1}, e''_{1}, e'_{2}, f'_{2}, g'_{2}, h'_{2}, b'_{1}, i''_{1}, j''_{1}, c'_{1}
  43. Rotate(A'_{1}, 90°, A) → K
  44. Rotate(E'_{2}, 90°, A) → L
  45. Rotate(F'_{2}, 90°, A) → M
  46. Rotate(G'_{2}, 90°, A) → N
  47. Rotate(H'_{2}, 90°, A) → O
  48. Rotate(B'_{1}, 90°, A) → P
  49. Rotate(I''_{1}, 90°, A) → Q
  50. Rotate(J''_{1}, 90°, A) → R
  51. Rotate(C'_{1}, 90°, A) → S
  52. Rotate(J'_{2}, 90°, A) → T
  53. Rotate(I'_{2}, 90°, A) → U
  54. Rotate(D'_{1}, 90°, A) → V
  55. Rotate(H''_{1}, 90°, A) → W
  56. Rotate(G''_{1}, 90°, A) → Z
  57. Rotate(F''_{1}, 90°, A) → A_1
  58. Rotate(E''_{1}, 90°, A) → B_1
  59. Polygon(K, L, U, V, W, Z, A_1, B_1, M, N, O, P, Q, R, S, T) → poly3, k, t, u, v, w, z_1, a_1, b_1, l, m, n, o, p, q, r, s
  60. Rotate(A, (-(90°)), C) → A'_{2}
  61. Rotate(E, (-(90°)), C) → E'_{3}
  62. Rotate(F, (-(90°)), C) → F'_{3}
  63. Rotate(G, (-(90°)), C) → G'_{3}
  64. Rotate(H, (-(90°)), C) → H'_{3}
  65. Rotate(B, (-(90°)), C) → B'_{2}
  66. Rotate(I', (-(90°)), C) → I''_{2}
  67. Rotate(J', (-(90°)), C) → J''_{2}
  68. Rotate(C, (-(90°)), C) → C'_{2}
  69. Rotate(J, (-(90°)), C) → J'_{3}
  70. Rotate(I, (-(90°)), C) → I'_{3}
  71. Rotate(D, (-(90°)), C) → D'_{2}
  72. Rotate(H', (-(90°)), C) → H''_{2}
  73. Rotate(G', (-(90°)), C) → G''_{2}
  74. Rotate(F', (-(90°)), C) → F''_{2}
  75. Rotate(E', (-(90°)), C) → E''_{2}
  76. Polygon(A'_{2}, E'_{3}, I'_{3}, D'_{2}, H''_{2}, G''_{2}, F''_{2}, E''_{2}, F'_{3}, G'_{3}, H'_{3}, B'_{2}, I''_{2}, J''_{2}, C'_{2}, J'_{3}) → poly2'_{2}, a'_{2}, j'_{3}, i'_{3}, d'_{2}, h''_{2}, g''_{2}, f''_{2}, e''_{2}, e'_{3}, f'_{3}, g'_{3}, h'_{3}, b'_{2}, i''_{2}, j''_{2}, c'_{2}
  77. Rotate(A'_{2}, (-(90°)), C) → C_1
  78. Rotate(E'_{3}, (-(90°)), C) → D_1
  79. Rotate(F'_{3}, (-(90°)), C) → E_1
  80. Rotate(G'_{3}, (-(90°)), C) → F_1
  81. Rotate(H'_{3}, (-(90°)), C) → G_1
  82. Rotate(B'_{2}, (-(90°)), C) → H_1
  83. Rotate(I''_{2}, (-(90°)), C) → I_1
  84. Rotate(J''_{2}, (-(90°)), C) → J_1
  85. Rotate(C'_{2}, (-(90°)), C) → K_1
  86. Rotate(J'_{3}, (-(90°)), C) → L_1
  87. Rotate(I'_{3}, (-(90°)), C) → M_1
  88. Rotate(D'_{2}, (-(90°)), C) → N_1
  89. Rotate(H''_{2}, (-(90°)), C) → O_1
  90. Rotate(G''_{2}, (-(90°)), C) → P_1
  91. Rotate(F''_{2}, (-(90°)), C) → Q_1
  92. Rotate(E''_{2}, (-(90°)), C) → R_1
  93. Polygon(C_1, D_1, M_1, N_1, O_1, P_1, Q_1, R_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1) → poly4, c_1, q_1, r_1, s_1, o_1, t_1, f_2, g_2, d_1, e_1, j_1, k_1, l_1, m_1, n_1, p_1
  94. Rotate(C_1, (-(90°)), C) → S_1
  95. Rotate(D_1, (-(90°)), C) → T_1
  96. Rotate(E_1, (-(90°)), C) → U_1
  97. Rotate(F_1, (-(90°)), C) → V_1
  98. Rotate(G_1, (-(90°)), C) → W_1
  99. Rotate(H_1, (-(90°)), C) → Z_1
  100. Rotate(I_1, (-(90°)), C) → A_2
  101. Rotate(J_1, (-(90°)), C) → B_2
  102. Rotate(K_1, (-(90°)), C) → C_2
  103. Rotate(L_1, (-(90°)), C) → D_2
  104. Rotate(M_1, (-(90°)), C) → E_2
  105. Rotate(N_1, (-(90°)), C) → F_2
  106. Rotate(O_1, (-(90°)), C) → G_2
  107. Rotate(P_1, (-(90°)), C) → H_2
  108. Rotate(Q_1, (-(90°)), C) → I_2
  109. Rotate(R_1, (-(90°)), C) → J_2
  110. Polygon(S_1, T_1, E_2, F_2, G_2, H_2, I_2, J_2, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2) → poly4', h_2, d_2, e_2, k_2, l_2, m_2, n_2, p_2, i_2, u_1, v_1, w_1, j_2, a_2, b_2, c_2
  111. Rotate(A, 180°, D) → A'_{3}
  112. Rotate(E, 180°, D) → E'_{4}
  113. Rotate(F, 180°, D) → F'_{4}
  114. Rotate(G, 180°, D) → G'_{4}
  115. Rotate(H, 180°, D) → H'_{4}
  116. Rotate(B, 180°, D) → B'_{3}
  117. Rotate(I', 180°, D) → I''_{3}
  118. Rotate(J', 180°, D) → J''_{3}
  119. Rotate(C, 180°, D) → C'_{3}
  120. Rotate(J, 180°, D) → J'_{4}
  121. Rotate(I, 180°, D) → I'_{4}
  122. Rotate(D, 180°, D) → D'_{3}
  123. Rotate(H', 180°, D) → H''_{3}
  124. Rotate(G', 180°, D) → G''_{3}
  125. Rotate(F', 180°, D) → F''_{3}
  126. Rotate(E', 180°, D) → E''_{3}
  127. Polygon(A'_{3}, E'_{4}, I'_{4}, D'_{3}, H''_{3}, G''_{3}, F''_{3}, E''_{3}, F'_{4}, G'_{4}, H'_{4}, B'_{3}, I''_{3}, J''_{3}, C'_{3}, J'_{4}) → poly2'_{3}, a'_{3}, j'_{4}, i'_{4}, d'_{3}, h''_{3}, g''_{3}, f''_{3}, e''_{3}, e'_{4}, f'_{4}, g'_{4}, h'_{4}, b'_{3}, i''_{3}, j''_{3}, c'_{3}
  128. Rotate(A, 180°, B) → A'_{4}
  129. Rotate(E, 180°, B) → E'_{5}
  130. Rotate(F, 180°, B) → F'_{5}
  131. Rotate(G, 180°, B) → G'_{5}
  132. Rotate(H, 180°, B) → H'_{5}
  133. Rotate(B, 180°, B) → B'_{4}
  134. Rotate(I', 180°, B) → I''_{4}
  135. Rotate(J', 180°, B) → J''_{4}
  136. Rotate(C, 180°, B) → C'_{4}
  137. Rotate(J, 180°, B) → J'_{5}
  138. Rotate(I, 180°, B) → I'_{5}
  139. Rotate(D, 180°, B) → D'_{4}
  140. Rotate(H', 180°, B) → H''_{4}
  141. Rotate(G', 180°, B) → G''_{4}
  142. Rotate(F', 180°, B) → F''_{4}
  143. Rotate(E', 180°, B) → E''_{4}
  144. Polygon(A'_{4}, E'_{5}, I'_{5}, D'_{4}, H''_{4}, G''_{4}, F''_{4}, E''_{4}, F'_{5}, G'_{5}, H'_{5}, B'_{4}, I''_{4}, J''_{4}, C'_{4}, J'_{5}) → poly2'_{4}, a'_{4}, j'_{5}, i'_{5}, d'_{4}, h''_{4}, g''_{4}, f''_{4}, e''_{4}, e'_{5}, f'_{5}, g'_{5}, h'_{5}, b'_{4}, i''_{4}, j''_{4}, c'_{4}

AI 绘图提示语参考

在同一坐标系中先画一个正方形，由给定的四点形成其边与顶点。以该正方形的某个顶点为旋转中心，按 90° 进行多次旋转，依次得到围绕中心分布的对应顶点。再把这些旋转得到的点按顺序首尾相连形成一个由多个旋转方块拼接而成的复杂多边形拼花区域，覆盖中心周围与对边相邻的部分。最后再用同样的 90° 旋转继续扩展，得到在同一方向上进一步延伸的外侧顶点与边，从而呈现旋转正方形的镶嵌图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。