阿马西亚-贝亚齐特清真寺数学模型

阿马西亚-贝亚齐特清真寺数学模型
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2020-08-18 14:30
①本范例通过动态演示贝亚齐特清真寺的建筑几何特征,揭示其对称性与多边形构成;②涉及的核心数学概念包括多边形、对称变换、积分与极限;③作图要点运用了点、构造步骤、多边形、镜像等 GeoGebra 命令,通过参数化控制几何变换;④适合高中及以上学生用于解析几何与微积分的视觉化学习,也可用于建筑几何教学。

GeoGebra 命令及参数

  1. Point(xAxis) → O_6
  2. ConstructionStep() → stap
  3. Polygon((0, -0.5), (10.5, -0.5), (10.5, 13.5), (0, 13.5)) → vierhoek1, f, g, h, i
  4. Mirror(afbeelding4, yAxis) → afbeelding4'
  5. Mirror(afbeelding5, yAxis) → afbeelding5'
  6. Polygon(N, O, P, Q, R, S, T, U, V, W) → veelhoek1, n, w, o, p, q, r, s, t, u, v
  7. 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
  8. 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
  9. 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
  10. Mirror(L_1, yAxis) → Z_1
  11. Mirror(P_1, yAxis) → A_2
  12. Mirror(J_1, yAxis) → B_2
  13. Mirror(Q_1, yAxis) → C_2
  14. Mirror(R_1, yAxis) → D_2
  15. Mirror(S_1, yAxis) → E_2
  16. Mirror(T_1, yAxis) → F_2
  17. Mirror(U_1, yAxis) → G_2
  18. Mirror(V_1, yAxis) → H_2
  19. Mirror(W_1, yAxis) → I_2
  20. 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
  21. Mirror(C_1, yAxis) → J_2
  22. Mirror(H_1, yAxis) → K_2
  23. Mirror(A_1, yAxis) → L_2
  24. Mirror(I_1, yAxis) → M_2
  25. Mirror(J_1, yAxis) → N_2
  26. Mirror(K_1, yAxis) → O_2
  27. Mirror(L_1, yAxis) → P_2
  28. Mirror(M_1, yAxis) → Q_2
  29. Mirror(N_1, yAxis) → R_2
  30. Mirror(O_1, yAxis) → S_2
  31. 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
  32. Mirror(T, yAxis) → T'
  33. Mirror(Z, yAxis) → Z'
  34. Mirror(A_1, yAxis) → T_2
  35. Mirror(B_1, yAxis) → U_2
  36. Mirror(C_1, yAxis) → V_2
  37. Mirror(D_1, yAxis) → W_2
  38. Mirror(E_1, yAxis) → Z_2
  39. Mirror(F_1, yAxis) → A_3
  40. Mirror(V, yAxis) → V'
  41. Mirror(G_1, yAxis) → B_3
  42. 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'
  43. Mirror(N, yAxis) → N'
  44. Mirror(O, yAxis) → O'
  45. Mirror(P, yAxis) → P'
  46. Mirror(Q, yAxis) → Q'
  47. Mirror(R, yAxis) → R'
  48. Mirror(S, yAxis) → S'
  49. Mirror(T, yAxis) → T'_1
  50. Mirror(U, yAxis) → U'
  51. Mirror(V, yAxis) → V'_1
  52. Mirror(W, yAxis) → W'
  53. 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
  54. 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
  55. 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
  56. 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
  57. 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
  58. Mirror(Z_3, yAxis) → M_4
  59. Mirror(E_4, yAxis) → N_4
  60. Mirror(F_4, yAxis) → O_4
  61. Mirror(G_4, yAxis) → P_4
  62. Mirror(H_4, yAxis) → Q_4
  63. Mirror(I_4, yAxis) → R_4
  64. Mirror(J_4, yAxis) → S_4
  65. Mirror(K_4, yAxis) → T_4
  66. Mirror(B_4, yAxis) → U_4
  67. Mirror(L_4, yAxis) → V_4
  68. 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
  69. Mirror(Q_3, yAxis) → W_4
  70. Mirror(U_3, yAxis) → Z_4
  71. Mirror(V_3, yAxis) → A_5
  72. Mirror(W_3, yAxis) → B_5
  73. Mirror(Z_3, yAxis) → C_5
  74. Mirror(A_4, yAxis) → D_5
  75. Mirror(B_4, yAxis) → E_5
  76. Mirror(C_4, yAxis) → F_5
  77. Mirror(O_3, yAxis) → G_5
  78. Mirror(D_4, yAxis) → H_5
  79. 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
  80. Mirror(G_3, yAxis) → I_5
  81. Mirror(M_3, yAxis) → J_5
  82. Mirror(E_3, yAxis) → K_5
  83. Mirror(N_3, yAxis) → L_5
  84. Mirror(O_3, yAxis) → M_5
  85. Mirror(P_3, yAxis) → N_5
  86. Mirror(Q_3, yAxis) → O_5
  87. Mirror(R_3, yAxis) → P_5
  88. Mirror(S_3, yAxis) → Q_5
  89. Mirror(T_3, yAxis) → R_5
  90. 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
  91. Mirror(C_3, yAxis) → S_5
  92. Mirror(D_3, yAxis) → T_5
  93. Mirror(E_3, yAxis) → U_5
  94. Mirror(F_3, yAxis) → V_5
  95. Mirror(G_3, yAxis) → W_5
  96. Mirror(H_3, yAxis) → Z_5
  97. Mirror(I_3, yAxis) → A_6
  98. Mirror(J_3, yAxis) → B_6
  99. Mirror(K_3, yAxis) → C_6
  100. Mirror(L_3, yAxis) → D_6
  101. 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
  102. 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
  103. 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
  104. Mirror(B_7, yAxis) → V_7
  105. Mirror(C_7, yAxis) → W_7
  106. Mirror(D_7, yAxis) → Z_7
  107. Mirror(E_7, yAxis) → A_8
  108. Mirror(F_7, yAxis) → B_8
  109. Mirror(G_7, yAxis) → C_8
  110. Mirror(H_7, yAxis) → D_8
  111. Mirror(I_7, yAxis) → E_8
  112. Mirror(J_7, yAxis) → F_8
  113. Mirror(K_7, yAxis) → G_8
  114. Mirror(L_7, yAxis) → H_8
  115. Mirror(M_7, yAxis) → I_8
  116. Mirror(N_7, yAxis) → J_8
  117. Mirror(O_7, yAxis) → K_8
  118. Mirror(P_7, yAxis) → L_8
  119. Mirror(Q_7, yAxis) → M_8
  120. Mirror(R_7, yAxis) → N_8
  121. Mirror(S_7, yAxis) → O_8
  122. Mirror(T_7, yAxis) → P_8
  123. Mirror(U_7, yAxis) → Q_8
  124. 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
  125. 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
  126. 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}
  127. 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}
  128. Mirror(M_9, yAxis) → T_9
  129. Mirror(N_9, yAxis) → U_9
  130. Mirror(O_9, yAxis) → V_9
  131. Mirror(P_9, yAxis) → W_9
  132. Mirror(Q_9, yAxis) → Z_9
  133. Mirror(R_9, yAxis) → A_{10}
  134. Mirror(S_9, yAxis) → B_{10}
  135. 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}
  136. 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}
  137. Mirror(C_{10}, yAxis) → J_{10}
  138. Mirror(D_{10}, yAxis) → K_{10}
  139. Mirror(E_{10}, yAxis) → L_{10}
  140. Mirror(F_{10}, yAxis) → M_{10}
  141. Mirror(G_{10}, yAxis) → N_{10}
  142. Mirror(H_{10}, yAxis) → O_{10}
  143. Mirror(I_{10}, yAxis) → P_{10}
  144. 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 绘图提示语参考

这是一个展示对称性的多边形几何模型。图形由一个矩形为基础,通过多次镜像操作生成多个对称的多边形。构造顺序为:先绘制矩形,然后将其沿垂直轴镜像,再将镜像后的多边形进一步镜像,形成一系列对称的多边形结构。整体呈现建筑几何特征,适合用于分析对称变换和图形构造的视觉学习。
以上提示语为根据原始绘图命令整理而来,仅供参考。