Amasya Beyazit Mosque Geometry Model

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2020-08-18 14:30

In collections Fatin Uluengin - muqarnas

This example dynamically demonstrates the geometric features of the Amasya Beyazit Mosque, revealing its symmetry and polygonal structure. Core math concepts include polygons, symmetry transformations, integration, and limits. Construction highlights use GeoGebra commands like Point, ConstructionStep, Polygon, and Mirror for parametric control of geometric transformations. Suitable for high school and above students learning analytical geometry and calculus visually, or for architectural geometry education.

GeoGebra Commands & Parameters

Point(xAxis) → O_6
ConstructionStep() → stap
Polygon((0, -0.5), (10.5, -0.5), (10.5, 13.5), (0, 13.5)) → vierhoek1, f, g, h, i
Mirror(afbeelding4, yAxis) → afbeelding4'
Mirror(afbeelding5, yAxis) → afbeelding5'
Polygon(N, O, P, Q, R, S, T, U, V, W) → veelhoek1, n, w, o, p, q, r, s, t, u, v
Polygon(T, Z, A_1, B_1, C_1, D_1, E_1, F_1, V, G_1) → veelhoek2, t_1, g_1, z_1, a_1, b_1, c_1, d_1, e_1, f_1, v_1
Polygon(C_1, H_1, A_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1) → veelhoek3, j, o_1, h_1, k, i_1, j_1, k_1, l_1, m_1, n_1
Polygon(L_1, P_1, J_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1) → veelhoek4, l, w_1, p_1, m, q_1, r_1, s_1, b, u_1, c
Mirror(L_1, yAxis) → Z_1
Mirror(P_1, yAxis) → A_2
Mirror(J_1, yAxis) → B_2
Mirror(Q_1, yAxis) → C_2
Mirror(R_1, yAxis) → D_2
Mirror(S_1, yAxis) → E_2
Mirror(T_1, yAxis) → F_2
Mirror(U_1, yAxis) → G_2
Mirror(V_1, yAxis) → H_2
Mirror(W_1, yAxis) → I_2
Polygon(Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2) → veelhoek4', d, i_2, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2
Mirror(C_1, yAxis) → J_2
Mirror(H_1, yAxis) → K_2
Mirror(A_1, yAxis) → L_2
Mirror(I_1, yAxis) → M_2
Mirror(J_1, yAxis) → N_2
Mirror(K_1, yAxis) → O_2
Mirror(L_1, yAxis) → P_2
Mirror(M_1, yAxis) → Q_2
Mirror(N_1, yAxis) → R_2
Mirror(O_1, yAxis) → S_2
Polygon(J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2) → veelhoek3', j_2, s_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, r_2
Mirror(T, yAxis) → T'
Mirror(Z, yAxis) → Z'
Mirror(A_1, yAxis) → T_2
Mirror(B_1, yAxis) → U_2
Mirror(C_1, yAxis) → V_2
Mirror(D_1, yAxis) → W_2
Mirror(E_1, yAxis) → Z_2
Mirror(F_1, yAxis) → A_3
Mirror(V, yAxis) → V'
Mirror(G_1, yAxis) → B_3
Polygon(T', Z', T_2, U_2, V_2, W_2, Z_2, A_3, V', B_3) → veelhoek2', t', b_3, z', t_2, u_2, v_2, w_2, z_2, a_3, v'
Mirror(N, yAxis) → N'
Mirror(O, yAxis) → O'
Mirror(P, yAxis) → P'
Mirror(Q, yAxis) → Q'
Mirror(R, yAxis) → R'
Mirror(S, yAxis) → S'
Mirror(T, yAxis) → T'_1
Mirror(U, yAxis) → U'
Mirror(V, yAxis) → V'_1
Mirror(W, yAxis) → W'
Polygon(N', O', P', Q', R', S', T'_1, U', V'_1, W') → veelhoek1', n', w', o', p', q', r', s', t'_1, u', v'_1
Polygon(C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3) → veelhoek5, c_3, l_3, d_3, e_3, f_3, g_3, h_3, i_3, j_3, k_3
Polygon(G_3, M_3, E_3, N_3, O_3, P_3, Q_3, R_3, S_3, T_3) → veelhoek6, e, f_4, m_3, n_3, p_3, o_3, q_3, r_3, s_3, t_3
Polygon(Q_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, O_3, D_4) → veelhoek7, g_4, d_4, u_3, v_3, w_3, z_3, a_4, b_4, c_4, h_4
Polygon(Z_3, E_4, F_4, G_4, H_4, I_4, J_4, K_4, B_4, L_4) → veelhoek8, i_4, r_4, e_4, j_4, k_4, l_4, m_4, n_4, p_4, q_4
Mirror(Z_3, yAxis) → M_4
Mirror(E_4, yAxis) → N_4
Mirror(F_4, yAxis) → O_4
Mirror(G_4, yAxis) → P_4
Mirror(H_4, yAxis) → Q_4
Mirror(I_4, yAxis) → R_4
Mirror(J_4, yAxis) → S_4
Mirror(K_4, yAxis) → T_4
Mirror(B_4, yAxis) → U_4
Mirror(L_4, yAxis) → V_4
Polygon(M_4, N_4, O_4, P_4, Q_4, R_4, S_4, T_4, U_4, V_4) → veelhoek8', s_4, v_4, t_4, o_4, f_5, g_5, h_5, i_5, j_5, u_4
Mirror(Q_3, yAxis) → W_4
Mirror(U_3, yAxis) → Z_4
Mirror(V_3, yAxis) → A_5
Mirror(W_3, yAxis) → B_5
Mirror(Z_3, yAxis) → C_5
Mirror(A_4, yAxis) → D_5
Mirror(B_4, yAxis) → E_5
Mirror(C_4, yAxis) → F_5
Mirror(O_3, yAxis) → G_5
Mirror(D_4, yAxis) → H_5
Polygon(W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → veelhoek7', w_4, m_5, z_4, a_5, b_5, c_5, d_5, e_5, k_5, l_5
Mirror(G_3, yAxis) → I_5
Mirror(M_3, yAxis) → J_5
Mirror(E_3, yAxis) → K_5
Mirror(N_3, yAxis) → L_5
Mirror(O_3, yAxis) → M_5
Mirror(P_3, yAxis) → N_5
Mirror(Q_3, yAxis) → O_5
Mirror(R_3, yAxis) → P_5
Mirror(S_3, yAxis) → Q_5
Mirror(T_3, yAxis) → R_5
Polygon(I_5, J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5) → veelhoek6', n_5, h_6, p_5, q_5, r_5, s_5, t_5, o_5, f_6, g_6
Mirror(C_3, yAxis) → S_5
Mirror(D_3, yAxis) → T_5
Mirror(E_3, yAxis) → U_5
Mirror(F_3, yAxis) → V_5
Mirror(G_3, yAxis) → W_5
Mirror(H_3, yAxis) → Z_5
Mirror(I_3, yAxis) → A_6
Mirror(J_3, yAxis) → B_6
Mirror(K_3, yAxis) → C_6
Mirror(L_3, yAxis) → D_6
Polygon(S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, D_6) → veelhoek5', i_6, d_6, j_6, u_5, v_5, w_5, z_5, a_6, b_6, c_6
Polygon(O_6, E_6, N_6, Q_6, Z_6, R_6, W_6, S_6, V_6, T_6, P_6, A_7, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6) → veelhoek9, k_6, e_6, f_7, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7, l_6, p_7, m_6, n_6, p_6, q_6, r_6, s_6, t_6
Polygon(B_7, C_7, L_7, M_7, N_7, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, D_7, E_7, F_7, G_7, H_7, I_7, J_7, K_7) → veelhoek10, b_7, f_8, g_8, h_8, i_8, o_7, j_8, k_8, l_8, m_8, n_8, c_7, u_7, d_7, e_7, q_7, r_7, s_7, t_7, a_7
Mirror(B_7, yAxis) → V_7
Mirror(C_7, yAxis) → W_7
Mirror(D_7, yAxis) → Z_7
Mirror(E_7, yAxis) → A_8
Mirror(F_7, yAxis) → B_8
Mirror(G_7, yAxis) → C_8
Mirror(H_7, yAxis) → D_8
Mirror(I_7, yAxis) → E_8
Mirror(J_7, yAxis) → F_8
Mirror(K_7, yAxis) → G_8
Mirror(L_7, yAxis) → H_8
Mirror(M_7, yAxis) → I_8
Mirror(N_7, yAxis) → J_8
Mirror(O_7, yAxis) → K_8
Mirror(P_7, yAxis) → L_8
Mirror(Q_7, yAxis) → M_8
Mirror(R_7, yAxis) → N_8
Mirror(S_7, yAxis) → O_8
Mirror(T_7, yAxis) → P_8
Mirror(U_7, yAxis) → Q_8
Polygon(V_7, W_7, H_8, I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8, Q_8, Z_7, A_8, B_8, C_8, D_8, E_8, F_8, G_8) → veelhoek10', v_7, q_8, r_8, s_8, t_8, f_9, g_9, h_9, i_9, o_8, j_9, w_7, k_9, z_7, a_8, b_8, c_8, d_8, e_8, p_8
Polygon(R_8, S_8, D_9, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9) → veelhoek11, l_9, c_9, d_9, m_9, n_9, u_8, v_8, w_8, z_8, a_9, b_9
Polygon(E_9, F_9, J_8, L_9, N_7, G_9, L_7, H_9, I_9, J_9, H_8, K_9) → veelhoek12, e_9, i_{10}, j_{10}, k_{10}, p_9, q_9, r_9, s_9, t_9, f_{10}, g_{10}, h_{10}
Polygon(M_9, N_9, O_9, P_9, Q_9, R_9, S_9) → veelhoek13, l_{10}, m_{10}, o_9, n_{10}, p_{10}, q_{10}, r_{10}
Mirror(M_9, yAxis) → T_9
Mirror(N_9, yAxis) → U_9
Mirror(O_9, yAxis) → V_9
Mirror(P_9, yAxis) → W_9
Mirror(Q_9, yAxis) → Z_9
Mirror(R_9, yAxis) → A_{10}
Mirror(S_9, yAxis) → B_{10}
Polygon(T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}) → veelhoek13', s_{10}, u_9, v_9, w_9, z_9, a_{10}, b_{10}
Polygon(C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}) → veelhoek14, c_{10}, d_{10}, e_{10}, t_{10}, f_{11}, g_{11}, h_{11}
Mirror(C_{10}, yAxis) → J_{10}
Mirror(D_{10}, yAxis) → K_{10}
Mirror(E_{10}, yAxis) → L_{10}
Mirror(F_{10}, yAxis) → M_{10}
Mirror(G_{10}, yAxis) → N_{10}
Mirror(H_{10}, yAxis) → O_{10}
Mirror(I_{10}, yAxis) → P_{10}
Polygon(J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}) → veelhoek14', i_{11}, j_{11}, k_{11}, l_{11}, m_{11}, o_{10}, n_{11}

AI Drawing Prompt Reference

This is a geometric model demonstrating symmetry. The figure consists of a rectangle as a base, then multiple symmetric polygons are generated through repeated mirroring. The construction order begins with drawing the rectangle, followed by mirroring it along the vertical axis, and then further mirroring the resulting polygons to create a series of symmetric polygon structures. The overall presentation reflects architectural geometry and is suitable for visual learning about symmetry transformations and geometric construction.

The prompt above was compiled from the original drawing commands and is for reference only.