旋转与向量几何构造

旋转与向量几何构造
几何画板及绘图内容加载中,请稍等……
2017-04-15 15:35
①本范例演示了利用旋转和向量构造多边形及其内切圆的几何过程;②涉及的核心数学概念包括旋转、向量运算、多边形构造、内切圆(或称内圆);③作图要点——从下方『构造摘要』提炼用到了Polygon(多边形)、Midpoint(中点)、Segment(线段)、Intersect(交点)、Circle(圆)、Point(点)等GeoGebra命令/对象;④适合高中数学教学或几何作图爱好者学习,有助于理解空间几何变换与图形性质。

GeoGebra 命令及参数

  1. Polygon(E, F, G, H) → poly2, e, f, g, h
  2. Polygon(I, K, L, M_2) → poly3, ı, k, l, m
  3. Midpoint(A, D) → N_2
  4. Midpoint(B, C) → O
  5. Midpoint(D, C) → P
  6. Midpoint(A, B) → Q
  7. Midpoint(E, F) → R
  8. Midpoint(G, H) → S
  9. Midpoint(E, H) → T
  10. Midpoint(F, G) → U
  11. Midpoint(K, L) → V
  12. Midpoint(I, M_2) → W
  13. Midpoint(M_2, L) → A_1
  14. Midpoint(I, K) → B_1
  15. Segment(N_2, O) → i
  16. Segment(Q, P) → j
  17. Segment(R, S) → n
  18. Segment(T, U) → p
  19. Segment(W, V) → q
  20. Segment(B_1, A_1) → r
  21. Intersect(i, j) → C_1
  22. Intersect(n, p) → D_1
  23. Intersect(q, r) → E_1
  24. Segment(K, L) → s
  25. Segment(C_1, D_1) → t
  26. Segment(E_1, D_1) → a_1
  27. Segment(E_1, C_1) → b_1
  28. Midpoint(C_1, D_1) → F_1
  29. Midpoint(C_1, E_1) → G_1
  30. Segment(D_1, G_1) → c_1
  31. Segment(F_1, E_1) → d_1
  32. Polygon(E_2, F_2, G_2, H_1) → poly2_1, e_1, f_1, g_1, h_1
  33. Midpoint(E_2, F_2) → R_1
  34. Midpoint(G_2, H_1) → S_1
  35. Midpoint(E_2, H_1) → T_1
  36. Midpoint(F_2, G_2) → U_1
  37. Segment(R_1, S_1) → n_1
  38. Segment(T_1, U_1) → p_1
  39. Intersect(n_1, p_1) → D_2
  40. Midpoint(C_1, E_1) → I_1
  41. Midpoint(D_2, D_1) → J_1
  42. Midpoint(D_1, E_1) → K_1
  43. Midpoint(C_1, D_2) → L_1
  44. Segment(I_1, J_1) → i_1
  45. Segment(L_1, K_1) → j_1
  46. Intersect(i_1, j_1) → M
  47. Circle(M, N) → k_1
  48. Point(k_1) → O_1
  49. Segment(O_1, A) → l_1
  50. Segment(O_1, D) → m_1
  51. Segment(O_1, B) → q_1
  52. Segment(O_1, C) → r_1
  53. Segment(O_1, I) → s_1
  54. Segment(O_1, M_2) → t_1
  55. Segment(O_1, K) → a_2
  56. Segment(O_1, L) → b_2
  57. Segment(O_1, H_1) → c_2
  58. Segment(O_1, E_2) → d_2
  59. Segment(O_1, F_2) → e_2
  60. Segment(O_1, G_2) → f_2
  61. Segment(O_1, H) → g_2
  62. Segment(O_1, E) → h_2
  63. Segment(O_1, F) → i_2
  64. Segment(O_1, G) → j_2
  65. Polygon(D, C, B, A) → poly1, d, c, b, a

AI 绘图提示语参考

画一个由多个多边形构成的图形,展示如何通过旋转和向量操作构建多边形及其内切圆。首先绘制几个多边形,然后找到各边的中点并连接,接着求出这些线段的交点,最后以这些交点为顶点构建新的多边形,并以内切圆展示其几何性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。