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Erzurum Hatuniye Madrassa Mirror Polygon Geometric Construction

Erzurum Hatuniye Madrassa Mirror Polygon Geometric Construction
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2020-08-18 13:39
PolygonTransformationGeometric Construction
In collections Fatin Uluengin - muqarnas
This GeoGebra example uses the architectural geometry of Erzurum Hatuniye Madrassa in Turkey to demonstrate the generation of symmetric figures through reflection and polygon construction. Core mathematical concepts include axial symmetry (reflection transformation), correspondence of polygon vertices and edges, congruent figures, and symmetry principles in geometric construction. The construction employs GeoGebra's Mirror command to reflect points, images, and polygons, and the Polygon command to create polygon1 and polygon2. Objects such as points A, B, C, segments d, e, f, and the image object afbeelding1 with its reflected image afbeelding1' are used to build the original figure and its mirror image, producing a symmetric architectural ornament pattern. Suitable for middle school and high school geometry instruction, teacher courseware development, and student independent exploration of transformational geometry.

GeoGebra Commands & Parameters

  1. Mirror(afbeelding1, yAxis) → afbeelding1'
  2. Polygon(D, E, F, G, H, I, J, K, C) → veelhoek1, d, e, f, g, h, i, j, k, c
  3. Polygon(L, M, N, O, P, Q, R, S) → veelhoek2, l, m, n, o, p, q, r, s
  4. Polygon(T, U, V, W, Z) → veelhoek3, t, u, v, w, z_1
  5. Polygon(T_1, U_1, V_1, W_1, Z_1) → veelhoek3_1, t_1, u_1, v_1, w_1, z_2
  6. Polygon(T_2, U_2, V_2, W_2, Z_2) → veelhoek3_2, t_2, u_2, v_2, w_2, z_3
  7. Polygon(T_3, U_3, V_3, W_3, Z_3) → veelhoek3_3, t_3, u_3, v_3, w_3, z_4
  8. Polygon(T_4, U_4, V_4, W_4, Z_4) → veelhoek3_4, t_4, u_4, v_4, w_4, z_5
  9. Polygon(T_5, U_5, V_5, W_5, Z_5) → veelhoek3_5, t_5, u_5, v_5, w_5, z_6
  10. Polygon(E_1, A_1, B_1, C_1, D_1) → veelhoek4, e_1, a_1, b_1, c_1, d_1
  11. Mirror(E_1, yAxis) → F_1
  12. Mirror(A_1, yAxis) → G_1
  13. Mirror(B_1, yAxis) → H_1
  14. Mirror(C_1, yAxis) → I_1
  15. Mirror(D_1, yAxis) → J_1
  16. Polygon(F_1, G_1, H_1, I_1, J_1) → veelhoek4', f_1, g_1, h_1, i_1, j_1
  17. Polygon(K_1, L_1, M_1, N_1, O_1) → veelhoek5, k_1, l_1, m_1, n_1, o_1
  18. Mirror(K_1, yAxis) → P_1
  19. Mirror(L_1, yAxis) → Q_1
  20. Mirror(M_1, yAxis) → R_1
  21. Mirror(N_1, yAxis) → S_1
  22. Mirror(O_1, yAxis) → A_2
  23. Polygon(P_1, Q_1, R_1, S_1, A_2) → veelhoek5', p_1, q_1, r_1, s_1, a_2
  24. Polygon(B_2, C_2, D_2, E_2, F_2) → veelhoek6, b_2, c_2, d_2, e_2, f_2

AI Drawing Prompt Reference

Draw a mirror-symmetric geometric figure based on the architectural geometry of Erzurum Hatuniye Madrassa in Turkey. Start with a point A and a line segment d, then reflect them across the y-axis to get A' and d'. Next, draw a polygon called polygon1 with points D, E, F, G, H, I, J, K, and C. Then draw another polygon called polygon2 with points L, M, N, O, P, Q, R, and S. Continue drawing multiple polygons called polygon3 through polygon6, each formed by points T, U, V, W, Z and their reflected points. All polygons should be symmetric about the y-axis to create a symmetric architectural ornament pattern. Ensure the figure is clear and shows symmetry and geometric construction relationships.
The prompt above was compiled from the original drawing commands and is for reference only.