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任意凹四边形中的角平分线奇妙关系

任意凹四边形中的角平分线奇妙关系
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2017-07-27 09:16
多边形角变换
这个范例展示了任意凹四边形中角平分线的动态关系。核心数学概念包括角平分线和多边形。通过旋转、角度、射线等GeoGebra命令构建，适合高中几何学习。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Rotate(A, α / 2, B) → A'_2
  4. Ray(B, A'_2) → r
  5. Ray(B, A') → g
  6. Point(g) → C
  7. Segment(B, C) → h
  8. Polygon(B, A, C) → poly1, c, b, a_1
  9. PointIn(poly1) → D
  10. Segment(C, D) → i
  11. Segment(D, A) → j
  12. Angle(B, C, D) → β
  13. Rotate(B, β / 2, C) → B'
  14. Ray(C, B') → l
  15. Angle(D, A, B) → γ
  16. Rotate(D, γ / 2, A) → D'
  17. Ray(A, D') → n
  18. Intersect(n, l) → J
  19. Segment(C, J) → g_1
  20. Segment(J, A) → h_1
  21. Segment(A, B) → f
  22. Min({f, i, h, j, g_1, h_1}) → d
  23. Circle(B, (0.2 * d)) → p
  24. Intersect(p, r, 1) → N
  25. Circle(B, (2 * Distance[B, N])) → r_1
  26. Intersect(r_1, r) → O,
  27. Angle(A, D, C) → δ
  28. Circle(D, (0.2 * d)) → q
  29. Circle(C, (0.2 * d)) → e
  30. Circle(A, (0.2 * d)) → k
  31. Intersect(e, h, 1) → E
  32. Intersect(q, j, 1) → F
  33. Intersect(k, j, 1) → G
  34. Intersect(p, f, 1) → H
  35. Angle(B, C, B') → ε
  36. Rotate(A, δ / 2, D) → A'_1
  37. Angle(A, D, A'_1) → ζ
  38. Angle(D, A, D') → η
  39. Angle(A, B, A'_2) → θ
  40. Ray(D, A'_1) → m
  41. Intersect(k, n) → K,
  42. Intersect(q, m, 1) → L
  43. Intersect(e, l) → M,
  44. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], J) → A'_3
  45. Segment(A, A'_3) → s
  46. Polygon(B, A, D, C) → poly2, b_1, a_2, d_1, c_1
  47. CircleSector(A, G, K) → t
  48. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], J) → C'
  49. Segment(C, C') → f_1
  50. CircleSector(C, E, M) → e_1
  51. Rotate(t, If[2 < o ≤ 3, ((o - 2) * η), η], A) → t'
  52. Rotate(e_1, If[3 < o ≤ 4, ((o - 3) * ε), ε], C) → k_1
  53. Dilate(B, If[4 < o ≤ 5, 5 - o, 0], O) → B'_1
  54. Segment(B, B'_1) → i_1
  55. Dilate(D, If[5 < o ≤ 6, 6 - o, 0], L) → D'_1
  56. Segment(D, D'_1) → j_1
  57. CircleSector(B, H, N) → p_1
  58. CircleSector(D, F, L) → q_1
  59. Ray(D, L) → l_1
  60. Rotate(p_1, If[6 < o ≤ 7, ((o - 6) * θ), θ], B) → s_1
  61. Rotate(q_1, If[7 < o ≤ 8, ((o - 7) * ζ), ζ], D) → t_1
  62. Line(J, i_1) → m_1
  63. Circle(J, 3) → c_2
  64. Intersect(c_2, m_1, 2) → P
  65. Angle(A, J, P) → κ
  66. Dilate(B, If[8 < o ≤ 9, 9 - o, 0], J) → B'_2
  67. Vector(B, B'_2) → u
  68. Translate(s_1, u) → d_2
  69. Rotate(d_2, If[9 < o ≤ 10, ((-(o - 9)) * κ), (-κ)], J) → e_2
  70. Midpoint(J, C) → Q
  71. Dilate(D, If[10 < o ≤ 11, 11 - o, 0], Q) → D'_2
  72. Vector(D, D'_2) → v
  73. Translate(t_1, v) → f_2
  74. Dilate(Q, If[11 < o ≤ 12, 12 - o, 0], J) → Q'
  75. Rotate(A, θ, J) → A'_4
  76. Rotate(A'_3, θ, J) → R
  77. Segment(A'_4, R) → s'
  78. Line(Q', s') → n_1
  79. Vector(Q, Q') → w
  80. Translate(f_2, w) → g_2
  81. Line(J, l_1) → h_2
  82. Circle(J, 3) → k_2
  83. Intersect(k_2, h_2) → S, T
  84. Angle(A'_4, J, T) → ρ
  85. Rotate(g_2, If[11 < o ≤ 12, ((-(o - 11)) * ρ), (-ρ)], Q') → p_2