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费尔巴哈点动态演示

费尔巴哈点动态演示
几何画板及绘图内容加载中，请稍等……
2018-12-29 05:10
测试改名0圆几何作图轨迹
①本范例动态演示任意三角形费尔巴哈点的性质；②涉及核心数学概念包括三角形、内切圆、中点、角平分线、圆交点等；③构造要点提炼自命令摘要，使用Segment, Rotate, Circle, Intersect, Polygon, Incircle, Midpoint等命令；④适合高中及以上数学学习者，用于理解费尔巴哈点与九点圆的关系，以及几何作图的动态变化。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Polygon(A, B, C) → t1, c, a_1, b
  7. Segment(A, B) → h
  8. Segment(B, C) → i
  9. Segment(C, A) → j
  10. Incircle(A, B, C) → d
  11. Midpoint(j) → D
  12. Midpoint(h) → E
  13. Midpoint(i) → F
  14. OrthogonalLine(C, h) → k
  15. OrthogonalLine(B, j) → l
  16. OrthogonalLine(A, i) → m
  17. Intersect(k, l) → G
  18. LineBisector(h) → n
  19. LineBisector(i) → p
  20. LineBisector(j) → q
  21. Line(A, B) → r
  22. Line(B, C) → s
  23. Line(C, A) → t
  24. Intersect(m, s) → H
  25. Intersect(l, t) → I
  26. Intersect(k, r) → J
  27. Midpoint(G, B) → K
  28. Midpoint(G, C) → L
  29. Midpoint(G, A) → M
  30. Circle(L, K, M) → e
  31. Intersect(d, e) → N, O, ,
  32. Segment(N, D) → f_1
  33. Segment(N, F) → g_1
  34. Segment(N, E) → h_1
  35. Max({f_1, g_1, h_1}) → u
  36. Circle(N, g_1) → c_1
  37. Intersect(c_1, f_1, 1) → P
  38. Angle(F, N, D) → β
  39. Line(P, h_1) → i_1
  40. Rotate(N, If[0 < v ≤ 1, (v * β), β], N) → N'
  41. Rotate(F, If[0 < v ≤ 1, (v * β), β], N) → F'
  42. Segment(N', F') → j_1
  43. Dilate(N', If[1 < v ≤ 2, 2 - v, 0], F') → N''
  44. Vector(N, N'') → w
  45. Translate(N, w) → N'_1
  46. Translate(E, w) → E'
  47. Segment(N'_1, E') → k_1
  48. Line(F', h_1) → l_1
  49. Point(l_1) → Q
  50. Angle(D, F', Q) → γ
  51. Rotate(N'_1, If[2 < v ≤ 3, ((-(v - 2)) * γ), (-γ)], F') → R
  52. Rotate(E', If[2 < v ≤ 3, ((-(v - 2)) * γ), (-γ)], F') → E''
  53. Segment(R, E'') → m_1
  54. Segment(N, F) → n_1
  55. Segment(N, E) → p_1
  56. Segment(N, D) → q_1
  57. Circle(N, E) → d_1
  58. Intersect(d_1, n_1, 1) → S
  59. Angle(E, N, S) → δ
  60. Rotate(N, If[0 < v ≤ 1, (v * δ), δ], N) → N'_2
  61. Rotate(E, If[0 < v ≤ 1, (v * δ), δ], N) → E'_1
  62. Segment(N'_2, E'_1) → r_1
  63. Dilate(N, If[1 < v ≤ 2, 2 - v, 0], E'_1) → N'_3
  64. Vector(N, N'_3) → u_1
  65. Translate(N, u_1) → N'_4
  66. Translate(D, u_1) → D'
  67. Segment(N'_4, D') → s_1
  68. Angle(F, N, D) → ε
  69. Rotate(N'_4, If[2 < v ≤ 3, ((-(v - 2)) * ε), (-ε)], E'_1) → T
  70. Rotate(D', If[2 < v ≤ 3, ((-(v - 2)) * ε), (-ε)], E'_1) → D''
  71. Segment(T, D'') → t_1
  72. Segment(N, E) → b_1
  73. Segment(N, F) → e_1
  74. Segment(N, D) → f_2
  75. Angle(D, N, E) → ζ
  76. Rotate(N, If[0 < v ≤ 1, (v * ζ), ζ], N) → N'_5
  77. Rotate(D, If[0 < v ≤ 1, (v * ζ), ζ], N) → D'_1
  78. Segment(N'_5, D'_1) → g_2
  79. Dilate(N, If[1 < v ≤ 2, 2 - v, 0], D'_1) → N'_6
  80. Vector(N, N'_6) → v_1
  81. Translate(N, v_1) → N'_7
  82. Translate(F, v_1) → F'_1
  83. Segment(N'_7, F'_1) → h_2
  84. Angle(D'_1, N, F) → η
  85. Rotate(N'_7, If[2 < v ≤ 3, ((-(v - 2)) * η), (-η)], D'_1) → W
  86. Rotate(F'_1, If[2 < v ≤ 3, ((-(v - 2)) * η), (-η)], D'_1) → Z
  87. Segment(W, Z) → i_2