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旋转木马模型

旋转木马模型
几何画板及绘图内容加载中，请稍等……
2020-07-17 00:23
变换几何作图
所属专题 Action Modular Origami
该范例演示了来自《Action Modular Origami》一书的纸模型动画。涉及的核心数学概念包括几何作图和变换。通过使用GeoGebra命令如Point, Intersect, Segment等，构建了一个旋转木马模型。适合用于几何作图和变换的教学。

GeoGebra 命令及参数

  1. Point(xAxis) → D
  2. Intersect(xAxis, yAxis) → A
  3. Segment(A, D) → h
  4. Point(h) → C
  5. Midpoint(C, D) → F
  6. OrthogonalLine(A, xOyPlane) → g
  7. Point(g) → E
  8. Plane(A, D, E) → a
  9. Rotate(C, α, F, a) → C'
  10. Rotate(D, α, F, a) → D'
  11. Rotate(G, α, F, a) → G'
  12. OrthogonalLine(G', g, a) → j
  13. Intersect(j, g) → H
  14. If(x(G') - x(H) < 0, x(G') - x(H), 0) → shift
  15. Vector(((-shift), 0, 0)) → u
  16. Translate(C', u) → C''
  17. OrthogonalLine(C'', a) → l
  18. Translate(D', u) → D''
  19. Segment(C'', D'') → m
  20. OrthogonalLine(D'', a) → k
  21. Translate(G', u) → G''
  22. Rotate(a, 15°, g) → a'
  23. Intersect(l, a') → K
  24. Mirror(K, a) → K'
  25. Line(K', K) → m_1
  26. Intersect(k, a') → J
  27. Plane(K, K', J) → b
  28. Mirror(J, a) → J'
  29. Midpoint(K', J') → L
  30. Circle(J', L, b) → q
  31. Intersect(m, q) → M, N
  32. OrthogonalLine(N, m_1, b) → p_1
  33. Intersect(p_1, l) → T
  34. Circle(K', L, b) → r
  35. Intersect(m, r) → R,
  36. Polygon(G'', J, J') → poly6, j'_1, g''_3, j_2
  37. Polygon(G'', K, J) → poly3, j_1, g'', k_1
  38. Polygon(K, If[Defined[R], R, T], G'') → poly7, q_1, r_1, s_1
  39. Polygon(If[Defined[R], R, T], K', G'') → poly8, t_1, a_1, b_1
  40. Polygon(J, N, G'') → poly10, g''_7, j_3, n_1
  41. Polygon(N, G'', J') → poly9, h_1, i_1, l_1
  42. Polygon(G'', K, K') → poly5, k'_1, g''_2, k_2
  43. Polygon(G'', K', J') → poly4, j', g''_1, k'
  44. Circle(A, C) → c
  45. Circle(A, D) → d
  46. Line(A, B) → f
  47. OrthogonalLine(F, f, a) → i
  48. Polygon(C, D, G) → poly1, g_1, c_1, d_1
  49. Polygon(G', C', D') → poly2, d', g', c'
  50. Translate(poly2, u) → poly2'
  51. Rotate(G, 15°, g) → G'_1
  52. Rotate(Rotate[G, 15°, g], α, F, a) → I
  53. Sequence(Rotate[{poly3, poly4, poly7, poly8, poly9, poly10}, (n * 30°), g], n, 0, 12, 2) → list1
  54. Mirror(list1, xOyPlane) → list1'
  55. Circle(K', J', b) → e
  56. Circle(J', K', b) → p
  57. Intersect(m, yAxis) → O
  58. Intersect(m, yAxis) → P
  59. Intersect(m, yAxis) → Q
  60. Segment(J', N) → n
  61. Segment(N, J) → s
  62. Segment(K', R) → t
  63. Segment(R, K) → f_1
  64. Intersect(l, m_1) → S
  65. Point(s22) → U
  66. Point(s22) → V
  67. Point(s2) → A_1
  68. Point(s2) → W
  69. Ray(V, A_1) → e_1
  70. Ray(U, W) → f_2
  71. Intersect(s3, g_2, (1.7, 1.8910065241883678)) → B_1
  72. Sequence(Rotate[{poly3, poly4, poly7, poly8, poly9, poly10}, (n * 30°), g], n, 1, 12, 2) → list2
  73. Mirror(list2, xOyPlane) → list2'