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抛物线特殊焦点弦动态演示

抛物线特殊焦点弦动态演示
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2017-05-04 06:25
向量解析几何几何作图
①本范例动态演示抛物线内部特殊焦点弦的几何性质；②涉及核心数学概念：抛物线、比例、三维向量、曲线绘制、二项分布、不定积分；③构造要点：运用了Line（线）、Parabola（抛物线）、Point（点）、OrthogonalLine（垂线）、Intersect（交点）、Dilate（缩放）、Segment（线段）、Angle（角度）、Rotate（旋转）、Circle（圆）、Ray（射线）等GeoGebra命令与对象；④适合高中及以上数学学习者和教师用于探索抛物线与焦点弦的动态关系及几何变换。

GeoGebra 命令及参数

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