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圆的旋转与相交动画

圆的旋转与相交动画
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2016-06-15 10:03
圆
该范例演示了圆的旋转与相交现象。涉及的核心数学概念包括圆、旋转、相交等。通过使用GeoGebra命令如Circle、Rotate、Intersect等，可以构造出动态的几何图形。适合初中及以上学生学习几何变换与动态几何。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. CircleArc(A, D, C) → d
  5. Point(d) → E
  6. Point(d) → F
  7. CircleArc(A, C, D) → e
  8. Segment(A, C) → a
  9. Segment(A, D) → b
  10. Segment(E, C) → f
  11. Segment(E, D) → g
  12. Segment(F, C) → h
  13. Segment(F, D) → i
  14. Angle(C, A, D) → α
  15. Rotate(C, α / 2, A) → C'
  16. Angle(C, A, C') → β
  17. Segment(A, C') → j
  18. Circle(E, (0.25 * Distance[A, B])) → k
  19. Intersect(k, f, 1) → G
  20. Intersect(k, g, 1) → H
  21. Circle(F, (0.25 * Distance[A, B])) → p
  22. Intersect(p, h, 1) → J
  23. Intersect(p, i, 1) → K
  24. CircleSector(E, G, H) → q
  25. CircleSector(F, J, K) → r
  26. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], A) → E'
  27. Vector(E, E') → u
  28. Translate(q, u) → q'
  29. Line(E, a) → m
  30. Intersect(k, m, 2) → L
  31. Angle(L, E, G) → γ
  32. Rotate(q', If[1 < l ≤ 2, ((-(l - 1)) * γ), (-γ)], A) → q''
  33. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], A) → E'_1
  34. Vector(E, E'_1) → v
  35. Translate(q, v) → q'_1
  36. Line(E, j) → n
  37. Intersect(k, n, 2) → M
  38. Angle(M, E, G) → δ
  39. Rotate(q'_1, If[3 < l ≤ 4, ((l - 3) * (360° - δ)), (-δ)], A) → s
  40. Circle(A, (0.25 * Distance[A, B])) → t
  41. Intersect(t, a, 1) → N
  42. Intersect(t, j, 1) → O
  43. Intersect(t, c, 1) → I
  44. Intersect(t, b) → P,
  45. CircleArc(A, N, P) → c_1