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Reuleaux三角形在菱形内的滚动

Reuleaux三角形在菱形内的滚动
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2018-09-25 21:39
测试改名0圆多边形轨迹
此演示展示Reuleaux三角形在菱形内的滚动运动与轨迹。核心涉及曲线几何、常宽三角形性质、圆弧构造与相对运动。作图要点包括使用Ray、Point、Rotate、Mirror、Circle、Intersect、Translate等GeoGebra命令，通过角度旋转、对称镜像、圆弧交点等构造三角形轨迹。适合高中几何、微积分极限过渡或参数方程单元的探究与可视化。

GeoGebra 命令及参数

  1. Ray(A, A') → aa'
  2. Point(aa') → B
  3. Rotate(B, (-betta), B) → B'
  4. Mirror(B, A) → BB
  5. Circle(BB, A) → bba
  6. Circle(A, B) → ab
  7. Intersect(ab, bba, 2) → D
  8. Rotate(D, (-betta), B) → D'
  9. Rotate(B, delta, D) → K
  10. Circle(K, K2) → kk2
  11. Translate(D', Vector[B, K]) → D''
  12. Translate(B', Vector[B, K]) → B''
  13. Ray(B'', D'') → bd''
  14. Intersect(kk2, bd'') → K1,
  15. Angle(K1, K, K2) → k
  16. Intersect(ab, bba, 1) → C
  17. Distance(C, D) → cd
  18. Vector(K, M) → km
  19. Translate(D, km) → D1
  20. Rotate(D1, k, M) → D2
  21. Translate(C, km) → C1
  22. Rotate(C1, k, M) → C2
  23. Translate(B, km) → B1
  24. Rotate(B1, k, M) → B2
  25. Translate(A, km) → A1
  26. Rotate(A1, k, M) → A2
  27. Ray(M, M') → mm'
  28. Point(mm') → N
  29. Rotate(N, π / 10, M) → N'
  30. Rotate(N, π / 2, M) → Q'
  31. CircleArc(M, N', Q') → nq'
  32. Point(nq') → Q
  33. OrthogonalLine(N, Line[M, Q]) → n
  34. Intersect(Line[M, Q], n) → L
  35. Distance(N, L) → nl
  36. Dilate(D2, c, M) → D3
  37. Dilate(C2, c, M) → C3
  38. Translate(C3, Vector[N, L]) → C4
  39. Dilate(B2, c, M) → B3
  40. Line(D3, B3) → d3b3
  41. Line(C4, d3b3) → c4
  42. Dilate(A2, c, M) → A3
  43. Line(A3, C3) → a3c3
  44. Ray(B, D) → bd
  45. Ray(B', D') → bd'
  46. Translate(N, Vector[M, Q]) → P
  47. PolyLine(M, N, P, Q, M) → m
  48. Line(B3, A3) → b3a3
  49. Circle(C3, B3) → c3b3
  50. Line(C3, D3) → c3d3
  51. Translate(B3, Vector[N, L]) → B4
  52. Line(B4, b3a3) → b4
  53. Intersect(c3d3, b4) → R
  54. AffineRatio(D3, C3, R) → dcr
  55. Dilate(B4, dcr1, D3) → B5
  56. AffineRatio(C3, D3, R) → cdr
  57. Dilate(B5, cdr1, C3) → B6
  58. Translate(B6, Vector[N, L]) → B7
  59. Line(B6, B7) → b6b7
  60. Intersect(a3c3, d3b3) → T
  61. Ray(C3, A3) → c3a3
  62. Intersect(c3b3, c3a3) → U,
  63. Intersect(a3c3, c4) → S
  64. AffineRatio(T, U, S) → tus
  65. Dilate(C4, tus1, U) → C5
  66. OrthogonalLine(C5, d3b3) → c5
  67. Intersect(d3b3, c5) → V
  68. AffineRatio(D3, B3, V) → dbv
  69. Dilate(C5, dbv1, D3) → C6
  70. OrthogonalLine(C6, b6b7) → c6
  71. Intersect(b6b7, c6) → E
  72. AffineRatio(B6, B7, E) → be
  73. Dilate(C6, be1, B6) → C7
  74. Intersect(Line[M, Q], b6b7) → F
  75. Translate(A3, Vector[C7, F]) → A4
  76. Line(A4, Line[M, Q]) → a4
  77. Line(A3, Line[M, N]) → a3
  78. Intersect(a3, a4) → G
  79. Translate(C3, Vector[A3, G]) → V2
  80. Translate(B3, Vector[A3, G]) → V1
  81. Translate(D3, Vector[A3, G]) → V3
  82. CircleArc(V1, V3, V2) → v132
  83. CircleArc(V2, V1, V3) → v213
  84. CircleArc(V3, V2, V1) → v321
  85. Distance(M, N) → d
  86. Line(I, xAxis) → i
  87. Point(i) → J
  88. Polygon({M, N, P, Q}) → m1
  89. CircleSector(V1, V3, V2) → v1
  90. CircleSector(V2, V1, V3) → v2
  91. CircleSector(V3, V2, V1) → v3