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十边形与五边形的伊斯兰几何图案

十边形与五边形的伊斯兰几何图案
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2019-12-31 16:06
多边形变换几何作图
这个范例演示了伊斯兰几何图案中的十边形与五边形。核心数学概念包括多边形的对称性。通过旋转、交点、射线等命令构造图案，适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. ConstructionStep() → stap
  2. Intersect(xAxis, yAxis) → A
  3. Point(xAxis) → B
  4. Rotate(B, 54°) → BB
  5. Ray(A, BB) → f
  6. OrthogonalLine(B, xAxis) → g
  7. Intersect(g, f) → C
  8. Polygon(A, B, C, D) → vierhoek1, a, b, c, d
  9. Centroid(vierhoek1) → E
  10. Segment(A, C) → h
  11. Segment(D, B) → i
  12. Angle(E, A, D) → α
  13. Angle(B, A, E) → β
  14. Midpoint(A, E) → F
  15. OrthogonalLine(F, h) → j
  16. Circle(F, G) → e
  17. Intersect(e, j, 2) → H
  18. Intersect(e, j, 1) → I
  19. Segment(H, I) → k
  20. Intersect(d, k) → J
  21. AngularBisector(E, A, D) → l
  22. Point(l) → K
  23. Segment(A, K) → m
  24. Intersect(k, m) → L
  25. AngularBisector(A, L, F) → n
  26. Point(n) → M
  27. Segment(L, M) → p
  28. Intersect(h, p) → N
  29. Circle(A, N) → q
  30. Circle(L, N) → r
  31. Intersect(q, r, 2) → O
  32. Polygon(O, N, 5) → veelhoek1, s, t, f_1, g_1, h_1, P, Q, R
  33. Polygon(P, N, 5) → veelhoek2, i_1, j_1, k_1, l_1, m_1, S, T, U
  34. Polygon(T, S, 5) → veelhoek3, n_1, p_1, q_1, r_1, s_1, V, W, Z
  35. Mirror(q, x = x(E)) → q'
  36. Mirror(q, y = y(E)) → q'_1
  37. Mirror(q, E) → q'_2
  38. Mirror(veelhoek1, x = x(E)) → veelhoek1'
  39. Mirror(veelhoek2, x = x(E)) → veelhoek2'
  40. Mirror(veelhoek3, x = x(E)) → veelhoek3'
  41. Mirror(veelhoek1, hor) → veelhoek1'_1
  42. Mirror(veelhoek2, hor) → veelhoek2'_1
  43. Mirror(veelhoek3, hor) → veelhoek3'_1
  44. Mirror(veelhoek1', hor) → veelhoek1''
  45. Mirror(veelhoek2', hor) → veelhoek2''
  46. Mirror(veelhoek3', hor) → veelhoek3''
  47. Polygon(P, U, 10) → veelhoek4, t_1, i_2, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, a_1, b_1, c_1, d_1, e_1, f_2, g_2, h_2
  48. Intersect(a, p_1) → I_1
  49. Intersect(a, xAxis) → J_1
  50. Intersect(a, xAxis) → K_1
  51. Mirror(I_1, ver) → L_1
  52. Mirror(I_1, hor) → M_1
  53. Mirror(L_1, hor) → N_1
  54. Intersect(a, xAxis) → O_1
  55. Mirror(Z, ver) → Z'
  56. Mirror(Z, hor) → Z'_1
  57. Mirror(Z', hor) → Z''
  58. Mirror(T, hor) → T'
  59. Mirror(S, ver) → S'
  60. Mirror(S', hor) → S''
  61. Mirror(S, hor) → S'_1
  62. Segment(S, I_1) → j_2
  63. Segment(S', L_1) → k_2
  64. Segment(S'_1, M_1) → l_2
  65. Segment(S'', N_1) → m_2