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正多边形的菱形分割探究

正多边形的菱形分割探究
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2017-06-01 04:54
多边形变换几何作图
本范例演示了正多边形如何通过菱形进行分割。涉及的核心数学概念包括多边形、菱形和变换。通过使用GeoGebra命令如Segment、Mirror、Polygon等，可以动态展示菱形分割的过程。适合初中及以上学生或教师用于几何教学。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Mirror(C, f) → C'
  3. Polygon(A, C, B, C') → poly1, a, c, b, c'
  4. Polygon(D, E, 12) → poly2, g, q, r, s, F, G, H, I, J, K, L, h, M, N, O, i, j, k, l, m, n, p
  5. los1(D, F, E) → poly3, P
  6. los1(D, N, O) → poly4, Q
  7. los1(Q, P, D) → poly5, R
  8. los1(N, R, Q) → poly6, S
  9. los1(R, F, P) → poly7, T
  10. los1(S, T, R) → poly8, U
  11. los1(M, S, N) → poly9, V
  12. los1(T, G, F) → poly10, W
  13. los1(V, U, S) → poly11, Z
  14. los1(U, W, T) → poly12, A_1
  15. Polygon(J, Z, U, A_1) → poly13, j_1, z_1, u, a_1
  16. Polygon(J, I, W, A_1) → poly14, j_2, i_1, w, a_2
  17. Polygon(I, H, G, W) → poly15, i_2, h_1, g_1, w_1
  18. Polygon(J, K, V, Z) → poly16, j_3, k_1, v, z_2
  19. Polygon(K, L, M, V) → poly17, k_2, l_1, m_1, v_1
  20. Polygon(M_2, N_2, 12) → poly35, q_2, g_3, h_3, i_3, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, r_2, V_2, W_2, Z_2, s_2, t_2, b_2, c_2, d_2, e_2, f_3
  21. Polygon(N_3, O_3, 12) → poly49, k_3, a_3, b_3, c_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, l_3, W_3, Z_3, A_4, m_3, n_3, p_3, q_3, r_3, s_3, t_3
  22. KITE(N_3, P_3, O_3) → B_4, poly50
  23. KITE(B_4, Q_3, P_3) → C_4, poly51
  24. KITE(N_3, C_4, B_4) → D_4, poly52
  25. KITE(A_4, D_4, N_3) → E_4, poly53
  26. KITE(Z_3, E_4, A_4) → F_4, poly54
  27. KITE(E_4, C_4, D_4) → G_4, poly55
  28. KITE(F_4, G_4, E_4) → H_4, poly56
  29. KITE(H_4, V_3, F_4) → I_4, poly57
  30. KITE(G_4, Q_3, C_4) → J_4, poly58
  31. KITE(H_4, J_4, G_4) → K_4, poly59
  32. KITE(U_3, K_4, T_3) → L_4, poly60
  33. KITE(J_4, R_3, Q_3) → M_4, poly61
  34. KITE(K_4, M_4, T_3) → N_4, poly62
  35. Polygon(B_1, C_1, 12) → poly18, t, t_1, b_1, c_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, d, K_1, L_1, M_1, e, f_1, n_1, p_1, q_1, r_1, s_1
  36. Polygon(N_1, O_1, 12) → poly19, d_1, q_4, r_4, s_4, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, e_1, W_1, Z_1, A_2, f_2, g_2, h_2, l_2, m_2, n_2, p_2
  37. KITE(C_1, E_1, D_1) → U_8, poly117
  38. KITE(C_1, M_1, B_1) → V_8, poly118
  39. KITE(L_1, V_8, M_1) → W_8, poly119
  40. KITE(K_1, W_8, L_1) → Z_8, poly120
  41. KITE(J_1, Z_8, K_1) → A_9, poly121
  42. KITE(A_9, I_1, J_1) → B_9, poly122
  43. KITE(A_9, G_1, H_1) → C_9, poly123
  44. KITE(C_9, F_1, G_1) → D_9, poly124
  45. KITE(D_9, E_1, F_1) → E_9, poly125
  46. KITE(D_9, C_1, U_8) → F_9, poly126
  47. Polygon(K_9, L_9, 6) → poly131, r_6, P_9, s_6, t_6, a_6, b_6, c_6, M_9, N_9, O_9
  48. Polygon(S_9, T_9, 7) → poly134, d_6, W_9, Z_9, A_{10}, e_6, f_7, g_7, h_7, i_7, j_7, U_9, V_9
  49. Polygon(B_{10}, C_{10}, 8) → poly135, k_7, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, l_7, m_7, n_7, p_7, q_7, r_7, s_7, D_{10}
  50. Polygon(J_{10}, K_{10}, 9) → poly136, t_7, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, a_7, b_7, c_7, d_7, e_7, f_8, g_8, h_8
  51. Polygon(S_{10}, T_{10}, 10) → poly137, i_8, s_8, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, j_8, k_8, l_8, m_8, n_8, p_8, q_8, r_8
  52. Polygon(E_{11}, F_{11}, 5) → poly138, t_8, a_8, b_8, c_8, d_8, G_{11}, H_{11}, I_{11}
  53. Polygon(U_{11}, V_{11}, 11) → poly150, e_8, n_9, p_9, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, f_9, G_{12}, g_9, h_9, i_9, j_9, k_9, l_9, m_9
  54. KITE(D_{14}, E_{14}, F_{14}) → G_{14}, poly184
  55. Segment(D_{14}, E_{14}) → i_{10}
  56. Segment(F_{14}, G_{14}) → j_{10}
  57. KITE(W_8, C_1, V_8) → B_2, poly20
  58. KITE(B_2, F_9, C_1) → C_2, poly21
  59. KITE(W_8, C_2, B_2) → D_2, poly22
  60. KITE(C_2, D_9, F_9) → E_2, poly23
  61. Polygon(F_2, G_2, 12) → poly24, d_3, m_4, n_4, p_4, H_2, I_2, J_2, K_2, L_2, A_3, B_3, e_3, C_3, D_3, E_3, f_4, g_4, h_4, i_4, j_4, k_4, l_4
  62. Polygon(F_3, G_3, 12) → poly25, t_4, i_5, j_5, k_5, H_3, I_3, J_3, K_3, L_3, M_3, O_4, a_4, P_4, Q_4, R_4, b_4, c_4, d_4, e_4, f_5, g_5, h_5
  63. Polygon(S_4, T_4, 12) → poly26, l_5, b_5, c_5, d_5, U_4, V_4, W_4, Z_4, A_5, B_5, C_5, m_5, D_5, E_5, F_5, n_5, p_5, q_5, r_5, s_5, t_5, a_5
  64. Polygon(G_5, H_5, 12) → poly27, e_5, n_6, p_6, q_6, I_5, J_5, K_5, L_5, M_5, N_5, O_5, f_6, P_5, Q_5, R_5, g_6, h_6, i_6, j_6, k_6, l_6, m_6
  65. Polygon(S_5, T_5, 12) → poly28, q_9, f_{10}, g_{10}, h_{10}, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, r_9, D_6, E_6, F_6, s_9, t_9, a_9, b_9, c_9, d_9, e_9