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Islamic Geometric Pattern Construction by chris cambré

Islamic Geometric Pattern Construction by chris cambré
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2019-12-31 17:27
PolygonTransformationGeometric Construction
This example demonstrates how to construct Islamic geometric patterns using rotation and reflection. Key math concepts include symmetry, multiplication, straight lines, rectangles, and quadrilaterals. Construction involves commands like Intersect, Rotate, Mirror, and more, suitable for high school mathematics education or geometric enthusiasts.

GeoGebra Commands & Parameters

  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