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两内切圆与内接等边三角形的动态演示

两内切圆与内接等边三角形的动态演示
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2018-03-11 12:22
测试改名0圆变换几何作图滑块动画
该范例展示了两个内切圆和一个内接等边三角形的动态关系。核心数学概念包括圆、等边三角形和几何变换。通过使用GeoGebra命令如Circle、Rotate、Intersect等，可以动态调整圆的大小和位置，观察等边三角形的变化。适合初中及以上学生学习几何变换和圆的相关性质。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → D
  3. Rotate(D, (2 * π / 3), A) → D'
  4. Rotate(D', (2 * π / 3), A) → D''
  5. CircleArc(A, D', D'') → s
  6. Point(s) → C
  7. Segment(A, C) → g
  8. Point(g) → F
  9. Semicircle(D'', F) → t
  10. Segment(F, C) → h
  11. Circle(F, h) → e
  12. Intersect(e, t, 1) → H
  13. Semicircle(D, F) → k
  14. Intersect(e, k, 1) → E
  15. Dilate(D'', If[6 < b ≤ 7, 7 - b, 0], H) → D'''
  16. Segment(D'', D''') → k_1
  17. Line(E, k_1) → p_1
  18. Point(p_1) → L
  19. Semicircle(D', F) → p
  20. Intersect(e, p, 1) → G
  21. Dilate(D', If[3 < b ≤ 4, 4 - b, 0], G) → D''_1
  22. Segment(D', D''_1) → f_1
  23. Line(D, f_1) → l_1
  24. Point(l_1) → S
  25. Polygon(D, D', D'') → t1, d'', d, d'
  26. Line(A, C) → f
  27. Segment(D, E) → i
  28. Segment(D', G) → j
  29. Semicircle(C, D'') → q
  30. Semicircle(D'', F) → r
  31. Segment(D'', H) → l
  32. Circle(D, j) → c_1
  33. Intersect(c_1, i) → I,
  34. Dilate(D, If[0 < b ≤ 1, 1 - b, 0], D') → D'_1
  35. Segment(D, D'_1) → m
  36. Rotate(D, If[1 < b ≤ 2, ((b - 1) * π / 3), π / 3], D) → D'_2
  37. Rotate(D'_1, If[1 < b ≤ 2, ((b - 1) * π / 3), π / 3], D) → J
  38. Segment(D'_2, J) → m'
  39. Rotate(D'_2, If[2 < b ≤ 3, ((b - 2) * π / 3), π / 3], D'') → K
  40. Rotate(J, If[2 < b ≤ 3, ((b - 2) * π / 3), π / 3], D'') → J'
  41. Segment(K, J') → m''
  42. Angle(D', G, F) → α
  43. Angle(D'', H, F) → β
  44. Angle(D, E, F) → γ
  45. Dilate(F, If[3 < b ≤ 4, 4 - b, 0], G) → F'
  46. Segment(F, F') → n
  47. Dilate(D, If[4 < b ≤ 5, 5 - b, 0], I) → D'_3
  48. Segment(D, D'_3) → g_1
  49. Dilate(I, If[5 < b ≤ 6, 6 - b, 0], E) → I'
  50. Segment(I, I') → h_1
  51. Dilate(F, If[5 < b ≤ 6, 6 - b, 0], E) → F'_1
  52. Segment(F, F'_1) → i_1
  53. Dilate(F, If[6 < b ≤ 7, 7 - b, 0], H) → F'_2
  54. Segment(F, F'_2) → j_1
  55. Angle(S, D, E) → δ
  56. Dilate(G, If[8 < b ≤ 9, 9 - b, 0], D) → G'
  57. Vector(G, G') → u
  58. Translate(D', u) → D''_2
  59. Translate(D''_1, u) → M
  60. Segment(D''_2, M) → m_1
  61. Rotate(D''_2, If[9 < b ≤ 10, ((b - 9) * δ), δ], D) → O
  62. Rotate(M, If[9 < b ≤ 10, ((b - 9) * δ), δ], D) → M'
  63. Segment(O, M') → n_1
  64. Angle(L, E, D) → ε
  65. Dilate(H, If[10 < b ≤ 11, 11 - b, 0], E) → H'
  66. Vector(H, H') → v
  67. Translate(D'', v) → D'''_1
  68. Translate(D''', v) → Q
  69. Segment(D'''_1, Q) → q_1
  70. Rotate(D'''_1, If[11 < b ≤ 12, ((b - 11) * ε), ε], E) → R
  71. Rotate(Q, If[11 < b ≤ 12, ((b - 11) * ε), ε], E) → Q'
  72. Segment(R, Q') → r_1