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动画演示多边形与三维向量

动画演示多边形与三维向量
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2016-06-14 22:44
多边形角向量立体几何几何作图
①本范例通过动画演示多边形与三维向量的关系，展示旋转、角度和三维空间中的几何变换；②涉及核心数学概念包括多边形构造、三维向量运算、角度测量、旋转变换等；③作图要点运用了Circle, Point, Line, Rotate, Angle, CircleArc, Ray, Intersect, CircleSector, Polygon等GeoGebra命令与对象；④适合高中及以上学段学习立体几何、向量与多边形性质的学生，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Circle(A, 8 - a) → c
  2. Point(c) → B
  3. Line(A, B) → b
  4. Rotate(B, 60°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 60°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 60°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 60°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 60°, A) → C'
  13. Angle(C, A, C') → ε
  14. CircleArc(A, B, B') → d
  15. CircleArc(A, B', B'') → e
  16. CircleArc(A, B'', B''') → f
  17. CircleArc(A, B''', C) → g
  18. CircleArc(A, C, C') → h
  19. CircleArc(A, C', B) → k
  20. Point(d) → D
  21. Point(e) → E
  22. Point(f) → F
  23. Point(g) → G
  24. Point(h) → H
  25. Point(k) → I
  26. Ray(D, E) → i
  27. Ray(E, F) → j
  28. Ray(F, G) → l
  29. Ray(G, H) → m
  30. Ray(H, I) → n
  31. Ray(I, D) → p
  32. Circle(E, 1.5) → q
  33. Circle(F, 1.5) → r
  34. Circle(G, 1.5) → s
  35. Circle(H, 1.5) → t
  36. Circle(I, 1.5) → c_1
  37. Circle(D, 1.5) → d_1
  38. Intersect(r, j, 1) → J
  39. Intersect(r, l, 1) → K
  40. Intersect(s, l, 2) → L
  41. Intersect(s, m, 1) → M
  42. Intersect(r, j, 2) → N
  43. Intersect(t, m, 2) → O
  44. Intersect(t, n, 1) → P
  45. Intersect(c_1, n, 2) → Q
  46. Intersect(c_1, p, 1) → R
  47. Intersect(d_1, p, 2) → S
  48. Intersect(d_1, i, 1) → T
  49. Intersect(q, j, 1) → U
  50. Intersect(q, i, 2) → V
  51. CircleSector(F, N, K) → e_1
  52. CircleSector(G, L, M) → f_1
  53. CircleSector(H, O, P) → g_1
  54. CircleSector(I, Q, R) → h_1
  55. CircleSector(D, S, T) → k_1
  56. CircleSector(E, V, U) → p_1
  57. Polygon(G, H, I, D, E, F) → poly1, g_2, h_2, i_1, d_2, e_2, f_2