平面多边形视角

平面多边形视角
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2015-02-05 15:30
该范例展示了多边形在平面上的视角。涉及的核心数学概念包括多边形、垂心、根、矩阵和复数。通过使用GeoGebra命令如Point、Polygon、Segment、Line等进行构造。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(yAxis) → E
  2. Point(yAxis) → D
  3. Polygon(D, E, 5) → poly2, P_S, e, f, g, h, F, G, H
  4. Segment(H, F) → k
  5. Line(J, F) → p
  6. Line(J, H) → n
  7. LineBisector(P_S) → j
  8. OrthogonalLine(G, j) → r
  9. Intersect(p, r) → N
  10. Intersect(n, r) → M
  11. Segment(M, N) → L_P
  12. Point(yAxis) → B
  13. Point(yAxis) → A
  14. Polygon(A, B, 3) → poly1, T_S, b, c, C
  15. LineBisector(T_S) → i
  16. Line(A, I) → l
  17. Line(B, I) → m
  18. OrthogonalLine(C, i) → q
  19. Intersect(l, q) → K
  20. Intersect(m, q) → L
  21. Segment(C, I) → D_T
  22. Segment(G, J) → D_P
  23. Segment(K, L) → L_T
  24. Segment(O, P) → a
  25. Segment(Q, R) → d
  26. Segment(A, I) → s
  27. Segment(I, B) → t
  28. Segment(H, J) → a_1
  29. Segment(J, F) → b_1
  30. Point(yAxis) → U
  31. Point(yAxis) → W
  32. Polygon(W, Z, 4) → poly3, c_1, d_1, e_1, f_1, A_1, B_1
  33. Line(W, A_1) → g_1
  34. Segment(B_1, C_1) → h_1
  35. Segment(Z, C_1) → i_1
  36. OrthogonalLine(A_1, g_1) → j_1
  37. Intersect(j_1, h_1) → D_1
  38. Intersect(j_1, i_1) → E_1
  39. Segment(D_1, E_1) → S_T
  40. Segment(A_1, C_1) → D_S
  41. Polygon(F_1, G_1, 6) → poly4, k_1, K_1, l_1, m_1, n_1, p_1, q_1, H_1, I_1, J_1
  42. Point(yAxis) → M_1
  43. Polygon(L_1, M_1, 7) → poly5, r_1, P_1, Q_1, R_1, s_1, t_1, a_2, b_2, c_2, d_2, N_1, O_1
  44. OrthogonalLine(P_1, r_1) → e_2
  45. Segment(G_1, I_1) → f_2
  46. LineBisector(f_2) → g_2
  47. Segment(I_1, T_1) → h_2
  48. Segment(G_1, T_1) → i_2
  49. OrthogonalLine(H_1, g_2) → j_2
  50. Intersect(j_2, h_2) → U_1
  51. Intersect(j_2, i_2) → V_1
  52. Segment(U_1, V_1) → k_2
  53. Segment(Q_1, S_1) → l_2
  54. Segment(O_1, S_1) → m_2
  55. Segment(R_1, S_1) → n_2
  56. Segment(S_1, N_1) → p_2
  57. Point(yAxis) → Z_1
  58. Polygon(W_1, Z_1, 8) → poly6, q_2, B_2, C_2, D_2, E_2, F_2, r_2, s_2, t_2, a_3, b_3, c_3, d_3, A_2
  59. Line(Z_1, D_2) → e_3
  60. Segment(E_2, G_2) → f_3
  61. Segment(G_2, C_2) → g_3
  62. Segment(B_2, G_2) → h_3
  63. Segment(F_2, G_2) → i_3
  64. Point(yAxis) → I_2
  65. Polygon(H_2, I_2, 9) → poly7, j_3, J_2, K_2, L_2, M_2, N_2, O_2, P_2, k_3, l_3, m_3, n_3, p_3, q_3, r_3, s_3
  66. LineBisector(j_3) → t_3
  67. Segment(N_2, Q_2) → a_4
  68. Segment(Q_2, L_2) → b_4
  69. Segment(K_2, Q_2) → c_4
  70. Segment(Q_2, O_2) → d_4

AI 绘图提示语参考

绘制一个平面上的多边形视图,包括三个不同大小的多边形。首先画一个五边形,然后画一个三角形,接着画一个四边形和一个六边形,最后画一个七边形。每个多边形都有其顶点和边,其中一些多边形之间有线段相连,形成特定的几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。