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Erzurum Hatuniye Madrassa Geometry Construction

Erzurum Hatuniye Madrassa Geometry Construction
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2020-08-18 13:36
PolygonAngleTrigonometryTransformationGeometric Construction
In collections Fatin Uluengin - muqarnas
This GeoGebra example demonstrates the construction of a geometric pattern inspired by the Hatuniye madrassa in Erzurum. Using commands such as Rotate, Mirror, and Circle, the construction builds a complex figure composed of polygons and circular arcs, illustrating the interplay between trigonometric concepts (e.g., cosine) and geometric transformations (e.g., dilation and scaling). Core mathematical ideas include angle measurement, orthogonal line construction, polygon incircles, and the use of midpoints and radii. The example is suitable for high‑school or early university students studying geometric constructions and coordinate geometry, and it can be used to show how mathematics informs architectural design.

GeoGebra Commands & Parameters

  1. ConstructionStep() → stap
  2. Rotate(O, 30°, N) → O'
  3. Ray(N, O') → f
  4. OrthogonalLine(O, xAxis) → g
  5. Intersect(g, f) → P
  6. OrthogonalLine(N, xAxis) → h
  7. OrthogonalLine(P, g) → i
  8. Intersect(h, i) → Q
  9. Polygon(Q, N, O, P) → vierhoek1, q, n, o, p
  10. Midpoint(N, O) → R
  11. OrthogonalLine(R, xAxis) → j
  12. Point(j) → S
  13. Point(j) → T
  14. Segment(S, T) → k
  15. Segment(Q, O) → l
  16. Segment(P, N) → m
  17. Angle(O, Q, P) → α
  18. Angle(Q, P, N) → β
  19. Intersect(p, k) → U
  20. Rotate(R, (-(30°)), U) → R'
  21. Ray(U, R') → r
  22. Intersect(n, r) → V
  23. Intersect(n, r) → W
  24. Mirror(V, k) → V'
  25. Segment(U, V) → s
  26. Segment(U, V') → t
  27. Angle(W, U, R) → ε
  28. Angle(R, U, V') → ζ
  29. Semicircle(V, V') → c
  30. Rotate(O, 15°, R) → O'_1
  31. Ray(R, O'_1) → a
  32. Intersect(o, a) → Z
  33. Intersect(c, a, 1) → A_1
  34. Segment(R, Z) → b
  35. Mirror(Z, k) → Z'
  36. Segment(R, Z') → d
  37. Rotate(O, 30°, R) → O'_2
  38. Angle(O, R, A_1) → η
  39. Ray(R, O'_2) → e
  40. Intersect(o, e) → C_1
  41. Segment(R, C_1) → f_1
  42. Mirror(C_1, k) → D_1
  43. Segment(R, D_1) → g_1
  44. Rotate(O, 45°, R) → O'_3
  45. Ray(R, O'_3) → h_1
  46. Intersect(o, h_1) → E_1
  47. Mirror(E_1, k) → F_1
  48. Segment(R, E_1) → i_1
  49. Segment(R, F_1) → j_1
  50. Rotate(O, 60°, R) → O'_4
  51. Ray(R, O'_4) → k_1
  52. Intersect(p, k_1) → I_1
  53. Mirror(I_1, k) → J_1
  54. Segment(R, I_1) → l_1
  55. Segment(R, J_1) → m_1
  56. Rotate(O, 75°, R) → O'_5
  57. Ray(R, O'_5) → n_1
  58. Intersect(p, n_1) → K_1
  59. Mirror(K_1, k) → L_1
  60. Segment(L_1, R) → p_1
  61. Segment(R, K_1) → q_1
  62. Intersect(c, d, 1) → B_1
  63. Intersect(c, i_1, 1) → M_1
  64. Intersect(c, j_1) → N_1,
  65. Intersect(c, q_1, 1) → O_1
  66. Intersect(c, p_1, 1) → P_1
  67. Mirror(P_1, k) → W_1
  68. Circle(B_1, G_1) → c_1
  69. Radius(c_1) → straal
  70. Intersect(c, j_1, 1) → H_1
  71. Circle(A_1, straal) → e_1
  72. Circle(H_1, straal) → d_1
  73. Circle(M_1, straal) → r_1
  74. Circle(P_1, straal) → s_1
  75. Circle(O_1, straal) → t_1
  76. Rotate(P, 45°, Z) → P'
  77. Ray(Z, P') → a_1
  78. Rotate(O, (-(45°)), P) → O'_6
  79. Ray(P, O'_6) → b_1
  80. Angle(P, Z, P') → γ
  81. Angle(O'_6, P, Z) → δ
  82. Point(a_1) → Q_1
  83. Point(b_1) → R_1
  84. Segment(Z, Q_1) → f_2
  85. Segment(P, R_1) → g_2
  86. Intersect(f_2, g_2) → S_1
  87. Circle(S_1, straal) → c_2
  88. Mirror(S_1, k) → T_1
  89. Mirror(P, k) → P'_1
  90. Mirror(R_1, k) → U_1
  91. Segment(P'_1, U_1) → h_2
  92. Mirror(Z, k) → Z'_1
  93. Mirror(Q_1, k) → V_1
  94. Segment(Z'_1, V_1) → i_2
  95. Circle(T_1, straal) → d_2

AI Drawing Prompt Reference

Draw a symmetric geometric pattern composed of a quadrilateral and circular arcs. Start with a horizontal baseline and a vertical line through a central point. Rotate a ray 30 degrees from the center to intersect another vertical line, forming a four-sided polygon. Use the midpoint of one side as a new center, draw a vertical line, and place two points on it to define a symmetry axis. Mirror some points and segments across this axis to create symmetry. From the center, draw rays at 15, 30, and 45 degrees to intersect the polygon sides and a semicircle, marking points and connecting them with radial segments. Finally, add a semicircle connecting two mirrored points to complete the design.
The prompt above was compiled from the original drawing commands and is for reference only.