积极 AI Logo 积极 AI

动画32：圆与向量变换

动画32：圆与向量变换
几何画板及绘图内容加载中，请稍等……
2016-06-17 01:33
圆向量变换
这个范例演示了如何通过向量变换和圆的几何性质来创建动态图形。核心数学概念包括圆、向量和几何变换。通过使用GeoGebra命令如Circle、Vector、Translate和Rotate，可以构造出复杂的几何图形。适合高中数学教学和学习，特别是解析几何和几何变换部分。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Segment(A, B) → a
  3. Point(c) → C
  4. Point(c) → D
  5. Segment(C, D) → d
  6. Point(d) → E
  7. CircleArc(A, C, D) → e
  8. Point(e) → F
  9. CircleArc(A, D, C) → f
  10. Ray(F, E) → b
  11. Intersect(f, b, 1) → G
  12. Segment(F, E) → g
  13. Segment(E, G) → h
  14. Segment(C, E) → i
  15. Segment(E, D) → j
  16. Min(list1) → k
  17. Circle(E, (0.4 * k)) → p
  18. Segment(A, G) → l
  19. Segment(A, C) → m
  20. Segment(A, F) → n
  21. Segment(A, D) → q
  22. Circle(A, (0.4 * k)) → r
  23. Intersect(r, l, 1) → H
  24. Intersect(r, m, 1) → I
  25. Intersect(p, h, 1) → J
  26. Intersect(p, i, 1) → K
  27. Intersect(p, g, 1) → L
  28. Intersect(p, j, 1) → M
  29. Intersect(r, n, 1) → N
  30. Intersect(r, q, 1) → O
  31. Angle(G, A, C) → α
  32. Angle(F, A, D) → β
  33. Rotate(G, (-(α / 2)), A) → G'
  34. Rotate(G, α / 2, A) → G'_1
  35. Angle(G, A, G'_1) → γ
  36. Rotate(F, β / 2, A) → F'
  37. Angle(F, A, F') → δ
  38. Segment(A, F') → s
  39. Segment(A, G'_1) → t
  40. Intersect(r, t, 1) → P
  41. Intersect(r, s, 1) → Q
  42. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], G) → A'
  43. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'_1
  44. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], F) → A'_2
  45. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'_3
  46. Segment(A, A') → a_1
  47. Segment(A, A'_1) → b_1
  48. Segment(A, A'_2) → c_1
  49. Segment(A, A'_3) → d_1
  50. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], G'_1) → A'_4
  51. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], F') → A'_5
  52. Segment(A, A'_4) → e_1
  53. Segment(A, A'_5) → f_1
  54. CircleSector(A, H, P) → g_1
  55. CircleSector(A, N, Q) → h_1
  56. Rotate(g_1, If[2 < o ≤ 3, ((o - 2) * γ), γ], A) → k_1
  57. CircleArc(A, H, P) → p_1
  58. Rotate(h_1, If[3 < o ≤ 4, ((o - 3) * δ), δ], A) → q_1
  59. CircleArc(A, N, Q) → r_1
  60. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], E) → A'_6
  61. Vector(A, A'_6) → u
  62. Translate(k_1, u) → s_1
  63. Translate(I, u) → I'
  64. Angle(I', E, K) → ε
  65. Rotate(s_1, If[5 < o ≤ 6, ((o - 5) * ε), ε], E) → t_1
  66. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], E) → A'_7
  67. Vector(A, A'_7) → v
  68. Translate(q_1, v) → c_2
  69. Angle(J, E, K) → ζ
  70. Translate(P, v) → P'
  71. Rotate(P', ε, E) → P''
  72. Translate(O, v) → O'
  73. Angle(O', E, P'') → η
  74. Rotate(c_2, If[7 < o ≤ 8, ((o - 7) * η), η], E) → d_2
  75. CircleArc(A, F, D) → e_2
  76. CircleArc(A, G, C) → f_2
  77. Intersect(p, h, 1) → R
  78. CircleSector(E, R, K) → g_2