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三维向量与几何变换动画演示

三维向量与几何变换动画演示
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2016-07-07 05:17
向量三角函数立体几何微积分几何作图
①本范例通过动画演示三维空间中圆、三角形、向量的关系及变换；②涉及核心数学概念包括三维向量、几何变换（旋转、平移）、相似与全等三角形、微积分应用；③构造中运用了Circle, Segment, PointIn, Tangent, Intersect, CircleArc, Point, Dilate, CircleSector, Line, Angle, Vector, Translate, Rotate, Polygon, OrthogonalLine等命令；④适合高中及以上学生及数学爱好者学习空间几何与向量知识，用于理解复杂几何现象。

GeoGebra 命令及参数

  1. Circle(A_1, B_1) → c
  2. Segment(A_1, B_1) → f
  3. PointIn(a_2) → C
  4. Tangent(C, c) → g, h
  5. Intersect(c, g) → D_1
  6. Intersect(c, h) → E_1
  7. CircleArc(A_1, D_1, E_1) → d
  8. Point(d) → A
  9. CircleArc(A_1, D_1, A) → e
  10. CircleArc(A_1, A, E_1) → k
  11. Point(k) → D
  12. CircleArc(A_1, E_1, D_1) → p
  13. Segment(C, A) → i
  14. Segment(C, D) → j
  15. Intersect(p, i, 1) → E
  16. Intersect(p, j, 1) → B
  17. Segment(D, E) → l
  18. Segment(B, A) → m
  19. CircleArc(A_1, B, E) → q
  20. CircleArc(A_1, E, D_1) → r
  21. CircleArc(A_1, E_1, B) → s
  22. Circle(D, (0.2 * f)) → t
  23. Circle(A, (0.2 * f)) → c_1
  24. Intersect(t, j, 1) → J
  25. Intersect(t, l, 1) → K
  26. Dilate(D, If[0 < b_2 ≤ 1, 1 - b_2, 0], E) → G'
  27. Segment(D, G') → n
  28. Dilate(B, If[1 < b_2 ≤ 2, 2 - b_2, 0], A) → I'
  29. Segment(B, I') → f_1
  30. CircleSector(D, J, K) → d_1
  31. Line(A, n) → g_1
  32. Intersect(c_1, g_1, 2) → L
  33. Intersect(c_1, i, 1) → M
  34. Angle(M, A, L) → α
  35. Dilate(D, If[2 < b_2 ≤ 3, 3 - b_2, 0], A) → G'_1
  36. Vector(D, G'_1) → u
  37. Translate(d_1, u) → e_1
  38. Rotate(e_1, If[3 < b_2 ≤ 4, ((-(b_2 - 3)) * α), (-α)], A) → h_1
  39. Circle(C, (0.2 * f)) → k_1
  40. Intersect(k_1, j, 1) → N
  41. Intersect(k_1, i, 1) → O
  42. CircleSector(C, O, N) → p_1
  43. Segment(A, E) → i_1
  44. Segment(E, C) → j_1
  45. Segment(D, B) → l_1
  46. Segment(B, C) → m_1
  47. Polygon(D, C, E) → poly1, h_2, g_2, c_2
  48. OrthogonalLine(E, i_1) → n_1
  49. OrthogonalLine(B, l_1) → q_1
  50. Circle(E, (0.1 * f)) → r_1
  51. Circle(B, (0.1 * f)) → s_1
  52. Intersect(s_1, q_1, 1) → P
  53. Intersect(r_1, n_1, 2) → Q
  54. Line(Q, i_1) → t_1
  55. Line(P, l_1) → a_1
  56. OrthogonalLine(A, t_1) → b_1
  57. OrthogonalLine(C, t_1) → f_2
  58. OrthogonalLine(D, a_1) → i_2
  59. OrthogonalLine(C, a_1) → j_2
  60. Intersect(t_1, b_1) → R
  61. Intersect(t_1, f_2) → S
  62. Intersect(a_1, j_2) → T
  63. Intersect(a_1, i_2) → U
  64. Dilate(R, If[4 < b_2 ≤ 5, 5 - b_2, 0], S) → R'
  65. Segment(R, R') → a
  66. Polygon(A, C, B) → poly2, i_3, f_3, c_3
  67. Dilate(U, If[5 < b_2 ≤ 6, 6 - b_2, 0], T) → U'
  68. Segment(U, U') → b
  69. Segment(C, E) → k_2
  70. Segment(C, B) → l_2
  71. CircleArc(A_1, B, E) → d_2