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整数平方的拼接

整数平方的拼接
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2017-10-22 05:05
多边形数列最值优化
①本范例演示如何用整数边长的正方形拼接平面；②涉及核心数学概念包括几何拼接、数列、最值优化；③构造要点：使用Polygon命令绘制正方形，通过A, B等对象定义顶点，利用f, g, h等函数和poly1, poly2等对象进行拼接；④适合初中及以上学生学习几何拼接与数列知识，也可用于探索空间填充问题。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  3. Polygon(I, J, 4) → poly3, n, p, q, r, K, L
  4. Polygon(M, N, 4) → poly4, s, t, a, b, O, P
  5. Polygon(Q, R, 4) → poly5, c, d, e, f_1, S, T
  6. Polygon(E_1, F_1, 4) → poly2_1, j_1, k_1, l_1, m_1, G_1, H_1
  7. Polygon(A_1, B_1, 4) → poly1_1, f_2, g_1, h_1, i_1, C_1, D_1
  8. Polygon(I_1, J_1, 4) → poly3_1, n_1, p_1, q_1, r_1, K_1, L_1
  9. Polygon(E_2, F_2, 4) → poly2_2, j_2, k_2, l_2, m_2, G_2, H_2
  10. Polygon(I_2, J_2, 4) → poly3_2, n_2, p_2, q_2, r_2, K_2, L_2
  11. Polygon(M_1, N_1, 4) → poly4_1, s_1, t_1, a_1, b_1, O_1, P_1
  12. Polygon(M_2, N_2, 4) → poly4_2, s_2, t_2, a_2, b_2, O_2, P_2
  13. Polygon(Q_1, R_1, 4) → poly5_1, c_1, d_1, e_1, f_3, S_1, T_1
  14. Polygon(Q_2, R_2, 4) → poly5_2, c_2, d_2, e_2, f_4, S_2, T_2
  15. Polygon(U, V, 4) → poly6, g_2, h_2, i_2, g_3, W, Z
  16. Polygon(U_1, V_1, 4) → poly7, h_3, i_3, j_3, k_3, W_1, Z_1
  17. Polygon(U_2, V_2, 4) → poly6_1, g_4, h_4, i_4, g_5, W_2, Z_2
  18. Polygon(M_3, N_3, 4) → poly4_3, s_3, t_3, a_3, b_3, O_3, P_3
  19. Polygon(E_3, F_3, 4) → poly2_3, j_4, k_4, l_3, m_3, G_3, H_3
  20. Polygon(M_4, N_4, 4) → poly4_4, s_4, t_4, a_4, b_4, O_4, P_4
  21. Polygon(U_3, V_3, 4) → poly6_2, g_6, h_5, i_5, g_7, W_3, Z_3
  22. Polygon(E_4, F_4, 4) → poly2_4, j_5, k_5, l_4, m_4, G_4, H_4
  23. Polygon(E_5, F_5, 4) → poly2_5, j_6, k_6, l_5, m_5, G_5, H_5
  24. Polygon(M_5, N_5, 4) → poly4_5, s_5, t_5, a_5, b_5, O_5, P_5
  25. Polygon(M_6, N_6, 4) → poly4_6, s_6, t_6, a_6, b_6, O_6, P_6
  26. Polygon(E_6, F_6, 4) → poly2_6, j_7, k_7, l_6, m_6, G_6, H_6
  27. Polygon(E_7, F_7, 4) → poly2_7, j_8, k_8, l_7, m_7, G_7, H_7
  28. Polygon(A_2, B_2, 4) → poly1_2, f_5, g_8, h_6, i_6, C_2, D_2
  29. Polygon(I_3, J_3, 4) → poly3_3, n_3, p_3, q_3, r_3, K_3, L_3
  30. Polygon(A_3, B_3, 4) → poly1_3, f_6, g_9, h_7, i_7, C_3, D_3
  31. Polygon(A_4, B_4, 4) → poly1_4, f_7, g_{10}, h_8, i_8, C_4, D_4
  32. Polygon(Q_3, R_3, 4) → poly5_3, c_3, d_3, e_3, f_8, S_3, T_3
  33. Polygon(I_4, J_4, 4) → poly8, n_4, p_4, q_4, r_4, K_4, L_4
  34. Polygon(Q_4, R_4, 4) → poly9, c_4, d_4, e_4, n_5, S_4, T_4
  35. Polygon(U_4, V_4, 4) → poly10, p_5, q_5, r_5, c_5, W_4, Z_4
  36. Polygon(Q_5, R_5, 4) → poly5_4, c_6, d_5, e_5, f_9, S_5, T_5
  37. Polygon(U_5, V_5, 4) → poly6_3, g_{11}, h_9, i_9, g_{12}, W_5, Z_5
  38. Polygon(U_6, V_6, 4) → poly6_4, g_{13}, h_{10}, i_{10}, g_{14}, W_6, Z_6
  39. Polygon(U_7, V_7, 4) → poly6_5, g_{15}, h_{11}, i_{11}, g_{16}, W_7, Z_7
  40. Polygon(U_8, V_8, 4) → poly7_1, h_{12}, i_{12}, j_9, k_9, W_8, Z_8
  41. Polygon(U_9, V_9, 4) → poly7_2, h_{13}, i_{13}, j_{10}, k_{10}, W_9, Z_9
  42. Polygon(U_{10}, V_{10}, 4) → poly7_3, h_{14}, i_{14}, j_{11}, k_{11}, W_{10}, Z_{10}
  43. Polygon(A_5, B_5, 4) → poly1_5, f_{10}, g_{17}, h_{15}, i_{15}, C_5, D_5
  44. Polygon(I_5, J_5, 4) → poly3_4, n_6, p_6, q_6, r_6, K_5, L_5