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正方形与八边形

正方形与八边形
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2019-03-21 00:43
多边形向量几何作图
所属专题 Cutting up squares
①本范例演示正方形与八边形的几何构造与关系；②涉及的核心数学概念包括多边形构造、向量运算、几何变换等；③作图要点运用了Intersect（交点）、Point（点）、Polygon（多边形）、Midpoint（中点）、Circle（圆）、Segment（线段）、Vector（向量）、Translate（平移）等GeoGebra命令；④适合高中数学教学，用于理解多边形性质与变换应用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Polygon(C, B, 8) → poly2, c_1, F, G, H, I, J, b_1, e, f, g, h, i, j, E
  5. Polygon(D, C, 8) → poly3, d_1, L, M, N, O, P, c_2, k, l, m, n, p, q, K
  6. Polygon(A, D, 8) → poly4, a_1, R, S, T, U, V, d_2, r, s, t, e_1, f_1, g_1, Q
  7. Polygon(B, A, 8) → poly5, b_2, Z, A_1, B_1, C_1, D_1, a_2, h_1, i_1, j_1, k_1, l_1, m_1, W
  8. Polygon(R, Q, 4) → poly7, r_1, q_1, s_1, t_1, G_1, H_1
  9. Polygon(D_1, C_1, 4) → poly9, d_3, c_3, g_2, h_2, K_1, L_1
  10. Midpoint(A, B_1) → I_3
  11. Midpoint(A, C) → J_3
  12. Circle(I_3, 0.7071067811865476) → t_5
  13. Circle(J_3, 1.5537739740300374) → c_6
  14. Midpoint(R, W) → K_3
  15. Midpoint(G_1, K) → L_3
  16. Midpoint(K, L_1) → M_3
  17. Circle(K_3, 0.7071067811865476) → d_6
  18. Circle(L_3, 0.7071067811865476) → e_6
  19. Circle(M_3, 0.7071067811865476) → f_6
  20. Intersect(t_5, c_6) → N_3, O_3, ,
  21. Intersect(d_6, c_6) → P_3, Q_3, ,
  22. Intersect(c_6, e_6) → R_3, S_3, ,
  23. Intersect(f_6, c_6) → T_3, U_3, ,
  24. Segment(R_3, U_3) → a_6
  25. Segment(U_3, O_3) → g_6
  26. Segment(O_3, Q_3) → i_6
  27. Segment(Q_3, R_3) → j_6
  28. Intersect(d_6, j_6, 2) → V_3
  29. Polygon(Q_3, V_3, 4) → poly22, q_6, v_3, k_6, l_6, W_3, Z_3
  30. Intersect(t_5, i_6, 2) → A_4
  31. Intersect(f_6, g_6, 2) → B_4
  32. Intersect(e_6, a_6, 2) → C_4
  33. Polygon(R_3, C_4, 4) → poly23, r_6, c_7, m_6, p_6, D_4, E_4
  34. Polygon(U_3, B_4, 4) → poly24, u_3, b_7, s_6, t_6, F_4, G_4
  35. Polygon(O_3, A_4, 4) → poly25, o_3, a_7, d_7, e_7, H_4, I_4
  36. Intersect(a_6, j) → E_1
  37. Intersect(g_6, b_1) → F_1
  38. Intersect(g_1, a_2) → I_1
  39. Intersect(j_6, q) → J_1
  40. Intersect(i_6, g_1) → M_1
  41. Polygon(R_3, E_1, C, D, J_1) → poly6, r_3, e_2, c_4, d_4, j_2
  42. Polygon(C, E_1, U_3, F_1, B) → poly8, c_5, e_3, u_1, f_2, b_3
  43. Polygon(B, F_1, O_3, M_1, A) → poly10, b_4, f_3, o_1, m_2, a_3
  44. Polygon(Q_3, M_1, A, D, J_1) → poly11, q_3, m_3, a_4, d_5, j_3
  45. Polygon(D, C, B, A) → poly12, d_8, c_8, b_5, a_5
  46. Vector(B, I) → u
  47. Translate(B, v1) → B'
  48. Translate(F_1, v1) → N_1
  49. Translate(O_3, v1) → O_1
  50. Translate(M_1, v1) → P_1
  51. Translate(A, v1) → A'
  52. Polygon(B', N_1, O_1, P_1, A') → poly10', b', n_1, o_2, p_1, a'
  53. Vector(A, G) → v
  54. Translate(Q_3, v2) → Q_1
  55. Translate(M_1, v2) → R_1
  56. Translate(A, v2) → A'_1
  57. Translate(D, v2) → D'
  58. Translate(J_1, v2) → S_1
  59. Polygon(Q_1, R_1, A'_1, D', S_1) → poly11', q_2, r_2, a'_1, d', s_2
  60. Vector(R_3, B_4) → w
  61. Translate(R_3, v3) → T_1
  62. Translate(E_1, v3) → U_1
  63. Translate(C, v3) → C'
  64. Translate(D, v3) → D'_1
  65. Translate(J_1, v3) → V_1
  66. Polygon(T_1, U_1, C', D'_1, V_1) → poly6', t_2, u_2, c', d'_1, v_1
  67. Polygon(J, I, 4) → poly13, j_4, i_2, k_2, l_2, W_1, Z_1
  68. Polygon(Z, V, 4) → poly14, z, v_2, n_2, p_2, A_2, B_2