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旋转圆与轨迹

旋转圆与轨迹
几何画板及绘图内容加载中，请稍等……
2017-06-09 03:36
圆变换轨迹
该范例演示了旋转圆与轨迹的概念。涉及的核心数学概念包括圆、旋转、轨迹等。通过使用GeoGebra命令如Circle、Rotate、Ray等，可以构造出动态的几何图形。适合高中几何与微积分课程使用。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(C, A) → f
  4. Intersect(c, f, 2) → D
  5. Rotate(D, ((-a) * π / 180), C) → D'
  6. Ray(C, D') → g
  7. Point(g) → E
  8. Midpoint(D, E) → F
  9. Line(F, D) → i
  10. OrthogonalLine(D, i) → j
  11. Intersect(c, j) → J, K
  12. CircleArc(A, K, D) → k
  13. Angle(D, C, D') → α
  14. Circle(F, E) → d
  15. Point(k) → G
  16. CircleArc(A, C, D) → e
  17. Ray(D, G) → h
  18. Intersect(d, h, 2) → H
  19. Midpoint(C, E) → I
  20. Distance(G, I) → distanceGI
  21. Distance(H, I) → distanceHI
  22. Polygon(C, E, D) → poly1, d_1, c_1, e_1
  23. Intersect(d, h) → L, M
  24. Distance(I, G) → distanceIG
  25. Distance(I, L) → distanceIL
  26. Segment(D, E) → l
  27. Dilate(C, If[0 < b ≤ 1, 1 - b, 0], I) → C'
  28. Segment(C, C') → m
  29. Rotate(C, If[1 < b ≤ 2, ((-(b - 1)) * π), (-π)], I) → C'_1
  30. Rotate(C', If[1 < b ≤ 2, ((-(b - 1)) * π), (-π)], I) → C''
  31. Segment(C'_1, C'') → m'
  32. Dilate(D, If[2 < b ≤ 3, 3 - b, 0], G) → D'_1
  33. Dilate(G, If[3 < b ≤ 4, 4 - b, 0], L) → G'
  34. Segment(D, D'_1) → n
  35. Segment(G, G') → p
  36. Line(D, G) → q
  37. Intersect(d, q) → N, O
  38. Distance(D, G) → o
  39. Distance(D, O) → r
  40. Dilate(D, If[2 < b ≤ 3, 3 - b, 0], L) → D'_2
  41. Segment(D, D'_2) → s
  42. Dilate(L, If[3 < b ≤ 4, 4 - b, 0], G) → L'
  43. Segment(L, L') → t
  44. Dilate(I, If[4 < b ≤ 5, 5 - b, 0], G) → I'
  45. Segment(I, I') → f_1
  46. Angle(L, I, G) → β
  47. Rotate(I, If[5 < b ≤ 6, ((-(b - 5)) * β), (-β)], I) → I'_1
  48. Rotate(I', If[5 < b ≤ 6, ((-(b - 5)) * β), (-β)], I) → I''
  49. Segment(I'_1, I'') → g_1
  50. Segment(C, D) → h_1