勾股定理装饰图案构造

勾股定理装饰图案构造
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2022-06-22 00:30
①本范例演示了如何利用勾股定理构造阿拉伯风格的几何装饰图案。②涉及的核心数学概念包括直角三角形、中点、圆、多边形构造、几何变换等。③作图要点:运用了Polygon(多边形)、Midpoint(中点)、Segment(线段)、Intersect(交点)、Circle(圆)、Point(点)、Line(直线)、Ray(射线)等GeoGebra命令与对象。④适合高中数学教学,用于展示几何作图技巧与变换应用。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → mnohoúhelník1, f, g, h, i, C, D
  2. Midpoint(A, B) → E
  3. Midpoint(C, D) → F
  4. Midpoint(D, A) → G
  5. Midpoint(B, C) → H
  6. Segment(G, H) → j
  7. Segment(E, F) → k
  8. Segment(A, C) → l
  9. Segment(D, B) → m
  10. Segment(G, F) → n
  11. Segment(F, H) → p
  12. Segment(H, E) → q
  13. Segment(E, G) → r
  14. Intersect(j, k) → I
  15. Circle(I, G) → c
  16. Intersect(c, l, 1) → J
  17. Point(c) → K
  18. Segment(J, K) → s
  19. Intersect(c, l, 2) → L
  20. Segment(K, L) → t
  21. Point(c) → M
  22. Segment(L, M) → a
  23. Segment(M, J) → b
  24. Segment(G, J) → d
  25. Segment(G, M) → e
  26. Segment(K, H) → f_1
  27. Segment(H, L) → g_1
  28. Intersect(r, b) → N
  29. Intersect(p, t) → O
  30. Segment(N, O) → h_1
  31. Intersect(n, b) → P
  32. Intersect(q, t) → Q
  33. Segment(P, Q) → i_1
  34. Segment(E, L) → j_1
  35. Segment(E, M) → k_1
  36. Segment(F, J) → l_1
  37. Segment(F, K) → m_1
  38. Line(N, O) → n_1
  39. Line(P, Q) → p_1
  40. Intersect(n_1, d) → R
  41. Segment(R, N) → q_1
  42. Intersect(p_1, e) → S
  43. Segment(P, S) → r_1
  44. Intersect(n_1, g_1) → T
  45. Segment(T, O) → s_1
  46. Intersect(p_1, f_1) → U
  47. Segment(U, Q) → t_1
  48. Segment(A, Q) → a_1
  49. Segment(O, D) → b_1
  50. Segment(N, B) → c_1
  51. Segment(P, C) → d_1
  52. Intersect(i_1, l_1) → V
  53. Intersect(l_1, b_1) → W
  54. Segment(V, W) → e_1
  55. Intersect(h_1, k_1) → Z
  56. Intersect(k_1, a_1) → A_1
  57. Segment(Z, A_1) → f_2
  58. Ray(S, M) → g_2
  59. Ray(R, J) → h_2
  60. Intersect(a_1, h_2) → B_1
  61. Segment(J, B_1) → i_2
  62. Intersect(b_1, g_2) → C_1
  63. Segment(C_1, M) → j_2
  64. Segment(C_1, W) → k_2
  65. Segment(B_1, A_1) → l_2
  66. Intersect(j_1, c_1) → D_1
  67. Intersect(i_1, j_1) → E_1
  68. Segment(D_1, E_1) → m_2
  69. Intersect(m_1, d_1) → F_1
  70. Intersect(h_1, m_1) → G_1
  71. Segment(F_1, G_1) → n_2
  72. Ray(T, L) → p_2
  73. Ray(U, K) → q_2
  74. Intersect(c_1, q_2) → H_1
  75. Segment(D_1, H_1) → r_2
  76. Segment(K, H_1) → s_2
  77. Intersect(d_1, p_2) → I_1
  78. Segment(L, I_1) → t_2
  79. Segment(I_1, F_1) → a_2
  80. Segment(A_1, E) → b_2
  81. Segment(E, D_1) → c_2
  82. Segment(W, F) → d_2
  83. Segment(F, F_1) → e_2
  84. Polygon(B_1, A_1, Z, R) → ct1, f_3, g_3, z_1, r_3
  85. Polygon(S, V, W, C_1) → ct2, s_3, v, w, h_3
  86. Polygon(G_1, T, I_1, F_1) → ct3, i_3, t_3, j_3, k_3
  87. Polygon(D_1, H_1, U, E_1) → ct4, l_3, m_3, u, n_3
  88. Polygon(E_1, I, Z, E) → ct5, p_3, i_4, z_2, e_3
  89. Polygon(V, I, G_1, F) → ct6, v_1, i_5, q_3, f_4
  90. Polygon(I, R, G, S) → ct7, i_6, r_4, g_4, s_4
  91. Polygon(I, U, H, T) → ct8, i_7, u_1, h_4, t_4
  92. Polygon(E, D_1, B) → t1, b_3, e_4, a_3
  93. Polygon(H_1, B, H) → t2, h_5, c_3, b_4
  94. Polygon(A, E, A_1) → t3, d_3, a_4, e_5
  95. Polygon(A, B_1, G) → t4, g_5, a_5, j_4
  96. Polygon(F, F_1, C) → t5, c_4, f_5, k_4
  97. Polygon(I_1, C, H) → t6, h_6, l_4, c_5
  98. Polygon(D, W, F) → t7, f_6, d_4, w_1
  99. Polygon(G, C_1, D) → t8, d_5, g_6, m_4

AI 绘图提示语参考

绘制一个由正方形和圆构成的阿拉伯风格几何装饰图案。首先绘制一个正方形,然后找到其对角线的中点,接着以这些中点为圆心绘制圆。利用这些圆和正方形的边,构造一系列相交的线段和圆弧,最终形成复杂的几何图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。