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线对称联动（别名：Imai蝴蝶)

线对称联动（别名：Imai蝴蝶)
几何画板及绘图内容加载中，请稍等……
2016-07-28 18:31
向量函数三角函数几何作图
①本范例演示线对称联动机构，即Imai蝴蝶的几何构造与运动特性；②涉及核心数学概念包括对称、几何变换、向量运算、函数图像及三维空间向量；③构造过程中运用了Circle（圆）、Intersect（交点）、Point（点）、Segment（线段）、Mirror（镜像）、Angle（角度）、Polygon（多边形）、Dilate（缩放）、Midpoint（中点）等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解几何变换、向量与函数图像的关联，以及探索复杂机械结构的对称性。

GeoGebra 命令及参数

  1. Circle(A, 2) → c
  2. Intersect(c, xAxis, 2) → A'
  3. Circle(A'_1, sqrt(2)) → q_1
  4. Point(c) → B
  5. Circle(A_1, 2) → s
  6. Segment(A_1, B_1) → i
  7. Circle(A_1, sqrt(2)) → q
  8. Intersect(q, i, 1) → F
  9. Circle(F, 2) → p_1
  10. Intersect(p_1, q_1, 2) → E
  11. Mirror(A'_1, E) → D
  12. Circle(D, 2) → r_1
  13. Circle(A_1, (2 * sqrt(2))) → s_1
  14. Intersect(r_1, s_1, 2) → C
  15. Segment(A_1, C) → l_1
  16. Segment(A, B) → f
  17. Mirror(B, xAxis) → B'
  18. Segment(A, B') → g
  19. Angle(A', A, B) → α
  20. Angle(B', A, A') → β
  21. Segment(A, A') → h
  22. Segment(A_1, A'_1) → j
  23. Circle(A'_1, (2 * sqrt(2))) → d
  24. Circle(A_1, (2 * sqrt(2))) → e
  25. Segment(A_1, C) → k
  26. Circle(C, 2) → p
  27. Segment(C, D) → l
  28. Segment(D, A'_1) → m
  29. Segment(A_1, A'_1) → n
  30. Segment(E, F) → r
  31. Polygon(A_1, F, E, A'_1) → poly1, a_1, f_1, e_1, a'_1
  32. Polygon(A_1, A'_1, D, C) → poly2, a_2, a'_2, d_1, c_1
  33. Intersect(s, l_1) → B'_1,
  34. Segment(B'_1, C) → t
  35. Segment(A_1, B'_1) → a
  36. Dilate(G, 1.5, H) → G'
  37. Dilate(G, 1.5, I) → G'_1
  38. Segment(G', H) → b
  39. Segment(I, G'_1) → g_1
  40. Circle(G'_1, G) → h_1
  41. Circle(G', G) → k_1
  42. Intersect(h_1, k_1, 2) → J
  43. Segment(J, G'_1) → i_1
  44. Segment(J, G') → j_1
  45. Segment(G, K) → m_1
  46. Midpoint(L, N) → O
  47. Segment(O, P) → t_1
  48. Segment(P, M) → b_1
  49. Segment(L, M) → f_2
  50. Segment(Q, O) → g_2
  51. Segment(Q, S) → h_2
  52. Segment(R, S) → i_2
  53. Segment(R, P) → j_2
  54. Segment(U, T) → k_2
  55. Segment(O, N) → n_1
  56. Segment(L, O) → l_2
  57. Circle(V, (0.5 * 2)) → c_2
  58. Segment(V, W) → m_2
  59. Point(c_2) → Z
  60. Circle(Z, (0.5 * 3)) → d_2
  61. Segment(V, Z) → n_2
  62. Intersect(d_2, m_2, 1) → C_1
  63. Segment(Z, C_1) → p_2
  64. Circle(C_1, (0.5 * 2)) → e_2
  65. Circle(V, (0.5 * 3)) → q_2
  66. Intersect(e_2, q_2, 2) → D_1
  67. Segment(V, D_1) → r_2
  68. Segment(D_1, C_1) → s_2
  69. Circle(V, (0.5 * 4 / 3)) → t_2
  70. Intersect(t_2, r_2, 1) → E_1
  71. Circle(Z, (0.5 * 4 / 3)) → c_3
  72. Circle(E_1, 1) → d_3
  73. Intersect(c_3, d_3, 2) → F_1
  74. Segment(Z, F_1) → b_2
  75. Segment(F_1, E_1) → f_3
  76. Polygon(F_1, Z, V, E_1) → poly3, f_4, z_1, v, e_3
  77. Angle(F_1, Z, V) → γ
  78. Angle(V, Z, C_1) → δ