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伊斯兰几何图案的构造 by chris cambré (2)

伊斯兰几何图案的构造 by chris cambré (2)
几何画板及绘图内容加载中，请稍等……
2019-12-31 17:27
多边形变换几何作图
①本范例演示了如何通过旋转和镜像构造伊斯兰几何图案；②涉及的核心数学概念包括对称性、乘法、直线、矩形、四边形等；③作图要点提炼了以下 GeoGebra 命令/对象：Intersect, ConstructionStep, Point, Segment, Rotate, Ray, Midpoint, Distance, Circle, Line, OrthogonalLine, CircleArc, Polygon, PolyLine, Mirror；④适合高中数学教学或几何爱好者学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Point(yAxis) → B
  4. Segment(A, B) → i
  5. Rotate(B, (3 / 7 * 90°)) → B'
  6. Ray(A, B') → g
  7. Intersect(f, g) → G
  8. Segment(G, A) → h
  9. Midpoint(h) → D
  10. Distance(A, D) → pas
  11. Circle(B, pas) → c
  12. Intersect(c, f, 1) → E
  13. Line(E, h) → j
  14. Intersect(j, i) → Z
  15. Segment(E, Z) → k
  16. Point(k) → T
  17. Line(T, f) → l
  18. Line(T, f) → m
  19. Point(m) → II
  20. Midpoint(E, T) → H
  21. Circle(T, H) → d
  22. Intersect(d, m, 2) → I
  23. Segment(T, I) → i_1
  24. Ray(E, I) → n
  25. ConstructionStep(I) → stapi
  26. Intersect(i, n) → K
  27. Segment(E, K) → p
  28. Line(K, f) → t
  29. Intersect(t, k) → L
  30. Segment(L, K) → a
  31. Segment(E, L) → b
  32. OrthogonalLine(K, k) → q
  33. CircleArc(Z, K, C_2) → e
  34. Intersect(e, q, 2) → N
  35. CircleArc(Z, K, N) → r
  36. Intersect(r, k, 1) → M
  37. Ray(L, N) → f_1
  38. Intersect(s, f_1) → S
  39. Segment(L, S) → g_1
  40. Circle(E, L) → c_1
  41. Intersect(c_1, f, 1) → O
  42. Rotate(N, (360°) / 7, S) → N'
  43. Polygon(N, N', 7) → veelhoek1, j_1, P, Q, R, k_1, l_1, m_1, n_1, p_1, q_1, F_2, J
  44. Intersect(s, p_1) → U
  45. PolyLine(U, R, N, N', F_2) → r_1
  46. Segment(S, O) → s_1
  47. Circle(O, Distance[N, S]) → d_1
  48. Intersect(d_1, s_1, 1) → V
  49. Rotate(V, ((-(360°))) / 7, O) → V'
  50. Polygon(V', V, 7) → veelhoek2, t_1, B_1, C_1, D_1, a_1, b_1, e_1, f_2, g_2, h_2, W, A_1
  51. Segment(O, S) → h_1
  52. Intersect(f, g_2) → E_1
  53. PolyLine(E_1, D_1, V', V, W) → i_2
  54. Midpoint(s_1) → F_1
  55. Mirror(A, x = x(F_1)) → F
  56. Mirror(B, x = x(F_1)) → C
  57. Segment(F, C) → i'
  58. ConstructionStep(i') → staplinks
  59. Segment(C, B) → j_2
  60. Segment(F, A) → k_2
  61. Ray(N', N) → l_2
  62. Intersect(k, l_2) → G_1
  63. Segment(N, G_1) → m_2
  64. Segment(G_1, K) → n_2
  65. Mirror(G_1, a) → H_1
  66. Mirror(K, a) → K'
  67. Segment(H_1, K') → p_2
  68. Ray(K, H_1) → q_2
  69. Line(H, k) → r_2
  70. Point(m_2) → I_1
  71. Line(I_1, m_2) → s_2
  72. Line(H, s_2) → t_2
  73. Intersect(t_2, q_2) → J_1
  74. Segment(K, J_1) → a_2
  75. Segment(Mirror[G_1, F_1], Mirror[K, F_1]) → KK
  76. Mirror(L, F_1) → L'
  77. Mirror(K, F_1) → K'_1
  78. Segment(L', K'_1) → a'
  79. Segment(L', O) → b_2
  80. Mirror(G_1, F_1) → K_1
  81. Segment(K_1, V) → c_2
  82. Mirror(V, x = x(W)) → V'_1
  83. Mirror(W, x = x(W)) → W'
  84. Segment(V'_1, W') → d_2
  85. Ray(W, V'_1) → e_2
  86. Intersect(t_2, e_2) → L_1
  87. Segment(L_1, J_1) → f_3
  88. Mirror(L_1, F_1) → M_1
  89. Mirror(J_1, F_1) → N_1
  90. Segment(M_1, N_1) → g_3
  91. Segment(K'_1, N_1) → h_3
  92. Segment(M_1, F_2) → i_3
  93. Mirror(H, F_1) → H'
  94. Ray(L', H') → j_3
  95. Intersect(k_2, j_3) → O_1
  96. Segment(L', O_1) → k_3
  97. OrthogonalLine(H, s_1) → l_3
  98. Mirror(L_1, l_3) → P_1
  99. Line(P_1, H) → m_3
  100. Line(R, N) → n_3
  101. Intersect(m_3, n_3) → Q_1
  102. Segment(Q_1, N) → p_3
  103. Intersect(m_3, j_2) → R_1
  104. Segment(Q_1, R_1) → q_3
  105. Mirror(Q_1, F_1) → S_1
  106. Mirror(R_1, F_1) → T_1
  107. Segment(S_1, T_1) → r_3
  108. Segment(V', S_1) → s_3
  109. Segment(W', L_1) → t_3
  110. Segment(O, E) → a_3
  111. Segment(O_1, S) → b_3