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伊斯兰几何图案构造

伊斯兰几何图案构造
几何画板及绘图内容加载中，请稍等……
2019-12-31 20:45
圆多边形立体几何变换几何作图
①本范例演示伊斯兰几何图案的构造过程；②涉及的核心数学概念包括对称性、多边形构造、旋转与反射变换；③作图要点：使用了Intersect（交点）、Point（点）、Circle（圆）、Rotate（旋转）、Polygon（多边形）、Dodecahedron（十二面体）、Centroid（重心）、Midpoint（中点）、Sphere（球）、CircleArc（圆弧）、Angle（角度）、Segment（线段）、Line（直线）、Mirror（镜像）等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解几何变换与图案设计。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, 72°) → C
  5. Polygon(B, C, 5) → veelhoek1, f, g, h, i, j, D, E, F
  6. Dodecahedron(veelhoek1, true) → a, G, P, Q, R, S, T, U, zijvlakBFJPK, zijvlakBCGLK, zijvlakCDHMG, zijvlakDEINH, H, zijvlakEFJOI, zijvlakJOTUP, zijvlakKLQUP, zijvlakGLQRM, zijvlakHMRSN, zijvlakINSTO, zijvlakQRSTU, RibbeBK, RibbeFJ, RibbeJP, I, RibbeKP, RibbeKL, RibbeGL, RibbeCG, RibbeGM, RibbeHM, RibbeDH, RibbeHN, RibbeIN, RibbeEI, J, RibbeIO, RibbeJO, RibbeOT, RibbeTU, RibbePU, RibbeQU, RibbeLQ, RibbeQR, RibbeMR, RibbeRS, K, RibbeNS, RibbeST, L, M, N, O
  7. Centroid(zijvlakQRSTU) → V
  8. Midpoint(A, V) → W
  9. Sphere(W, B) → b
  10. Midpoint(RibbeQU) → Z
  11. Midpoint(RibbeQR) → A_1
  12. Midpoint(RibbeRS) → B_1
  13. Midpoint(RibbeST) → C_1
  14. Midpoint(RibbeTU) → D_1
  15. CircleArc(W, U, Q) → d
  16. Angle(U, W, Q) → HoekUQ
  17. Segment(W, Q) → r
  18. Segment(U, W) → q
  19. CircleArc(W, Q, R) → e
  20. Line((0, 0, 0), (0, 0, 1)) → as
  21. Rotate(e, 72°, as) → e'
  22. Rotate(e, 144°, as) → e'_1
  23. Rotate(e, (-(144°)), as) → e'_2
  24. CircleArc(W, L, Q) → s
  25. CircleArc(W, P, U) → c_1
  26. CircleArc(W, K, L) → d_1
  27. CircleArc(W, P, K) → f_1
  28. CircleArc(W, O, T) → g_1
  29. CircleArc(W, O, J) → h_1
  30. CircleArc(W, J, P) → k_1
  31. CircleArc(W, N, S) → p_1
  32. CircleArc(W, N, I) → q_1
  33. CircleArc(W, I, O) → r_1
  34. CircleArc(W, I, E) → s_1
  35. CircleArc(W, H, N) → t_1
  36. CircleArc(W, M, H) → c_2
  37. CircleArc(W, M, R) → d_2
  38. CircleArc(W, J, F) → e_2
  39. CircleArc(W, K, B) → f_2
  40. CircleArc(W, L, G) → g_2
  41. CircleArc(W, G, C) → h_2
  42. CircleArc(W, G, M) → k_2
  43. CircleArc(W, H, D) → p_2
  44. CircleArc(W, D, E, xOyPlane) → r_2
  45. CircleArc(W, E, F) → s_2
  46. CircleArc(W, F, B) → t_2
  47. CircleArc(W, B, C) → c_3
  48. CircleArc(W, C, D) → d_3
  49. Midpoint(RibbeQU) → E_1
  50. Rotate(Q, 54°, Line[A_1, A_1 + (0, 0, 1)]) → Q'
  51. Rotate(R, 54°, Line[A_1, A_1 + (0, 0, 1)]) → R'
  52. Segment(Q', R') → RibbeQR'
  53. Rotate(R, (-(54°)), Line[B_1, B_1 + (0, 0, 1)]) → R'_1
  54. Rotate(S, (-(54°)), Line[B_1, B_1 + (0, 0, 1)]) → S'
  55. Segment(R'_1, S') → RibbeRS'
  56. Intersect(RibbeQR', RibbeRS') → F_1
  57. Segment(A_1, F_1) → k
  58. Segment(F_1, B_1) → l
  59. Rotate(seg, 72°, as) → seg'
  60. Rotate(seg', 72°, as) → seg''
  61. Rotate(seg', 144°, as) → seg''_1
  62. Rotate(seg', (-(144°)), as) → seg''_2
  63. Rotate(seg', (-(72°)), as) → seg''_3
  64. Mirror(ring, W) → ring'
  65. Centroid(zijvlakGLQRM) → G_1
  66. Line(W, G_1) → asas
  67. Rotate(ring, 72°, asas) → ring'_1
  68. Rotate(ring, 144°, asas) → ring'_2
  69. Rotate(ring, (-(144°)), asas) → ring'_3
  70. Rotate(ring, (-(72°)), asas) → ring'_4
  71. Rotate(ring'_1, 72°, as) → l1
  72. Rotate(ring'_1, (-(72°)), as) → l2
  73. Rotate(l2, (-(72°)), as) → l2'
  74. Rotate(ring'_3, 72°, as) → l3
  75. Rotate(l3, 72°, as) → l3'
  76. Rotate(l3, 144°, as) → l3'_1
  77. Intersect(Ray[W, F_1], b) → H_1,
  78. Segment(H_1, W) → m
  79. Intersect(Ray[W, A_1], b) → I_1,
  80. CircleArc(W, I_1, H_1) → p
  81. Intersect(Ray[W, B_1], b) → J_1,
  82. CircleArc(W, H_1, J_1) → t
  83. Rotate(hoekje, 72°, as) → hoekje'
  84. Rotate(hoekje', 144°, as) → hoekje''
  85. Rotate(hoekje', (-(72°)), as) → hoekje''_1
  86. Rotate(hoekje', 72°, as) → hoekje''_2
  87. Rotate(hoekje', (-(144°)), as) → hoekje''_3
  88. Rotate(bolring, 72°, asas) → bolring'
  89. Rotate(bolring, (-(72°)), asas) → bolring'_1
  90. Rotate(bolring, (-(144°)), asas) → bolring'_2
  91. Rotate(bolring, 144°, asas) → bolring'_3
  92. Rotate(bolring, 144°, asas) → bolring'_4
  93. Rotate(bolring', 72°, as) → bolring''
  94. Rotate(bolring', (-(72°)), as) → bolring''_1
  95. Rotate(bolring'_1, 72°, as) → l4
  96. Rotate(bolring'_2, 72°, as) → l5
  97. Rotate(bolring'_2, 144°, as) → l6
  98. Rotate(l6, 72°, as) → l6'
  99. Mirror(bolring, W) → bolring'_5