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等边三角形中的动态几何问题

等边三角形中的动态几何问题
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2018-01-02 11:02
测试改名0向量几何作图
这是一个动态可修改的等边三角形问题示例，由 Antonio Gutierrez 在 Twitter 上发布。该示例展示了等边三角形的基本性质和动态变换。通过使用 GeoGebra 的 Distance, PointIn, Line, Circle, Intersect, Rotate, CircleArc, OrthogonalLine, Point, Polygon, Semicircle, Segment, Angle, Dilate, Vector, Translate 等命令，可以直观地观察等边三角形的性质和变换。适合初中及以上学生学习几何变换和动态几何。

GeoGebra 命令及参数

  1. Distance(A, B) → a
  2. PointIn(b) → C
  3. Line(C, A) → f
  4. Circle(A, B) → c
  5. Intersect(c, f) → D, E
  6. Rotate(D, (-2 * π / 3), A) → D'
  7. Rotate(D', (-2 * π / 3), A) → D''
  8. CircleArc(A, D'', D') → q
  9. OrthogonalLine(D, f) → g
  10. Point(q) → F
  11. Rotate(F, (2 * π / 3), A) → F'
  12. Rotate(F', (2 * π / 3), A) → F''
  13. Polygon(F, F', F'') → t1, f'', f_1, f'
  14. Semicircle(C, F') → e
  15. Semicircle(F'', C) → h
  16. Intersect(d, e, 1) → I
  17. Intersect(d, h, 1) → J
  18. Segment(F', I) → i
  19. Segment(F'', J) → j
  20. Semicircle(F, C) → k
  21. Intersect(d, k, 1) → K
  22. Segment(F, K) → l
  23. Angle(F'', J, C) → α
  24. Angle(C, I, F') → β
  25. Angle(F, K, C) → γ
  26. Circle(F, i) → p
  27. Intersect(p, l, 1) → G
  28. Dilate(F, If[0 < n ≤ 1, 1 - n, 0], F') → F'_1
  29. Segment(F, F'_1) → r
  30. Rotate(F, If[1 < n ≤ 2, ((n - 1) * π / 3), π / 3], F) → F'_2
  31. Rotate(F'_1, If[1 < n ≤ 2, ((n - 1) * π / 3), π / 3], F) → H
  32. Segment(F'_2, H) → r'
  33. Rotate(F, If[2 < n ≤ 3, ((-(n - 2)) * π / 3), ((-π)) / 3], F') → F'_3
  34. Rotate(F'_1, If[2 < n ≤ 3, ((-(n - 2)) * π / 3), ((-π)) / 3], F') → L
  35. Segment(F'_3, L) → r'_1
  36. Dilate(C, If[3 < n ≤ 4, 4 - n, 0], I) → C'
  37. Dilate(F', If[3 < n ≤ 4, 4 - n, 0], I) → F''_1
  38. Segment(F', F''_1) → s
  39. Segment(C, C') → t
  40. Dilate(F'', If[4 < n ≤ 5, 5 - n, 0], J) → F'''
  41. Segment(F'', F''') → g_1
  42. Dilate(C, If[4 < n ≤ 5, 5 - n, 0], J) → C'_1
  43. Segment(C, C'_1) → h_1
  44. Dilate(F, If[5 < n ≤ 6, 6 - n, 0], G) → F'_4
  45. Segment(F, F'_4) → i_1
  46. Dilate(G, If[6 < n ≤ 7, 7 - n, 0], K) → G'
  47. Segment(G, G') → j_1
  48. Dilate(C, If[6 < n ≤ 7, 7 - n, 0], K) → C'_2
  49. Segment(C, C'_2) → k_1
  50. Dilate(F', If[8 < n ≤ 9, 9 - n, 0], F) → F''_2
  51. Vector(F', F''_2) → u
  52. Translate(F', u) → F''_3
  53. Translate(F''_1, u) → M
  54. Segment(F''_3, M) → s'
  55. Line(F', j_1) → l_1
  56. Point(l_1) → N
  57. Angle(I, F', N) → δ
  58. Rotate(F''_3, If[9 < n ≤ 10, ((n - 9) * δ), δ], F) → O
  59. Rotate(M, If[9 < n ≤ 10, ((n - 9) * δ), δ], F) → M'
  60. Segment(O, M') → s''
  61. Dilate(J, If[10 < n ≤ 11, 11 - n, 0], K) → J'
  62. Vector(J, J') → v
  63. Translate(F'', v) → F'''_1
  64. Translate(F''', v) → P
  65. Segment(F'''_1, P) → m_1
  66. Line(J, j_1) → n_1
  67. Point(n_1) → Q
  68. Angle(F'', J, Q) → ε
  69. Rotate(F'''_1, If[11 < n ≤ 12, ((n - 11) * ε), ε], K) → R
  70. Rotate(P, If[11 < n ≤ 12, ((n - 11) * ε), ε], K) → P'
  71. Segment(R, P') → p_1