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二维向量与几何图形构造

二维向量与几何图形构造
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2020-06-02 19:17
多边形向量几何作图
①本范例演示了利用二维向量和基本几何元素（圆、正方形、等边三角形）构建复杂图形的过程；②涉及的核心数学概念包括向量运算、线性回归、多边形构造、几何变换等；③作图要点提炼自构造摘要，用到了LineBisector（角平分线）、Vector（向量）、OrthogonalVector（正交向量）、Line（直线）、OrthogonalLine（垂线）、Mirror（镜像）、Intersect（交点）、Polygon（多边形）、CircumcircleArc（外接圆弧）、Midpoint（中点）等命令和对象；④适合高中及以上数学学习者，用于理解向量、几何变换及计算几何的综合应用。

GeoGebra 命令及参数

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A_1, A) → l
  5. Line(A, B) → s
  6. OrthogonalLine(Q, s) → q
  7. Mirror(q, m) → q'
  8. OrthogonalLine(D, s) → i
  9. Intersect(i, l) → P
  10. Mirror(i, m) → i'
  11. Intersect(i', l) → H
  12. OrthogonalLine(A, s) → b
  13. OrthogonalLine(J, b) → p
  14. Intersect(q', p) → L_1
  15. Line(H, L_1) → a
  16. Line(I, a) → f_1
  17. OrthogonalLine(F, b) → f
  18. Intersect(i, f) → R
  19. LineBisector(R, P) → n
  20. Intersect(n, i) → T
  21. Mirror(f, l) → f'
  22. Intersect(m, f') → S
  23. Line(K_1, f_1) → g_1
  24. Mirror(f, l) → f'_1
  25. Intersect(q', f'_1) → K
  26. OrthogonalLine(N, f') → h
  27. Intersect(h, g_1) → V
  28. OrthogonalLine(A_1, b) → r
  29. Intersect(i, f') → E
  30. OrthogonalLine(K_1, f'_1) → n_1
  31. Intersect(m, l) → L
  32. OrthogonalLine(B, u, xOyPlane) → g
  33. Intersect(g, r) → C
  34. Mirror(F, l) → F'
  35. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  36. Intersect(i', f') → W
  37. Mirror(p, l) → p'
  38. Intersect(i', f) → G_1
  39. Intersect(m, f) → G
  40. Line(H, L_1) → j
  41. Line(I, j) → k
  42. Intersect(h, k) → M
  43. CircumcircleArc(T, G, H) → c
  44. CircumcircleArc(T, U, I) → d
  45. CircumcircleArc(T, L, K_1) → t
  46. Intersect(t, f_1) → Z,
  47. CircumcircleArc(T, O, V) → e
  48. Intersect(e, f_1) → B_1,
  49. Midpoint(Z, B_1) → C_1
  50. Midpoint(L, O) → D_1
  51. CircumcircleArc(T, D_1, C_1) → c_1
  52. Intersect(d, a) → E_1,
  53. Intersect(e, a) → F_1,
  54. Vector(H, E_1) → w
  55. Polygon(K_1, V, B_1, C_1, T) → poly1, k_1, v_1, b_1, h_1, t_1
  56. CircumcircleArc(T, I_1, J_1) → p_1
  57. CircumcircleArc(T, O, F_1) → q_1
  58. Polygon(K_1, V, B_1, Z) → q1, i_1, v_2, j_1, z_1
  59. Intersect(t, a) → H_1,
  60. Polygon(C_1, Z, H_1) → t1, l_1, m_1, z_2
  61. Polygon(B_1, I, E_1, F_1) → q2, r_1, i_2, s_1, f_2
  62. Intersect(d, p') → M_1,
  63. Polygon(H, E_1, M_1) → t2, g_2, h_2, j_2