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Constructing the Ankara Arslanhane Mosque Mihrab using Geometry

Constructing the Ankara Arslanhane Mosque Mihrab using Geometry
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2020-08-18 13:59
Coordinate GeometryTransformationGeometric Construction
In collections Fatin Uluengin - muqarnas
This example demonstrates how to construct the mihrab (prayer niche) of the Arslanhane Mosque in Ankara using GeoGebra's Point, PolyLine, Segment, and Mirror tools. It focuses on geometric construction, symmetry, reflection transformations, and coordinate geometry operations. By defining key points, drawing polyline outlines, and applying mirror commands, users can quickly generate intricate Islamic geometric patterns. The example is suitable for high school geometry and plane geometry courses, as well as interdisciplinary projects combining art and mathematics.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_3
  2. Point(yAxis) → F
  3. PolyLine(C, D, E, F, G, H, I) → f
  4. PolyLine(J, K, L, M, A_3, N, O, P, Q) → g
  5. Point(g) → Z
  6. Point(yAxis) → B_3
  7. PolyLine(R, S, C_1, H_1, D_1, E_1, F_1, T, G_1, U, V, W, B_3, A_1, B_1) → h
  8. Point(yAxis) → Q_1
  9. PolyLine(I_1, J_1, Q_1, A_1, R_1, S_1, T_1, B_1, U_1, V_1, W_1, Z_1, K_1, A_2, L_1, M_1, V, N_1, O_1, P_1, W) → i
  10. Point(yAxis) → I_2
  11. PolyLine(I_1, B_2, J_2, K_2, L_2, M_2, N_2, O_2, W_1, P_2, A_2, K_1, C_2, D_2, E_2, F_2, G_2, H_2, I_2) → j
  12. PolyLine(I_1, Q_2, B_2, C_2, R_2, G_2) → k
  13. Segment(H_2, J_2) → l
  14. Mirror(I_1, yAxis) → S_2
  15. Mirror(Q_2, yAxis) → T_2
  16. Mirror(B_2, yAxis) → U_2
  17. Mirror(C_2, yAxis) → V_2
  18. Mirror(R_2, yAxis) → W_2
  19. Mirror(G_2, yAxis) → Z_2
  20. PolyLine(S_2, T_2, U_2, V_2, W_2, Z_2) → k'