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莱布尼茨抛物线 - 移动割线至切线位置

莱布尼茨抛物线 - 移动割线至切线位置
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2015-04-19 15:07
函数解析几何导数滑块动画轨迹
本范例通过移动滑块Y_1和Y_2，演示抛物线从割线到切线的转换过程。核心数学概念包括抛物线的性质和导数。使用了Line, Point, Parabola, Intersect, Segment, OrthogonalLine, Ray等GeoGebra命令。适合高中数学教学，特别是微积分和解析几何课程。

GeoGebra 命令及参数

  1. Line(A_1, B) → a
  2. Point(yAxis) → C
  3. Parabola(C, a) → c
  4. Point(c) → Y_1
  5. Point(c) → Y_2
  6. Intersect(c, xAxis, 1) → A
  7. Line(A, a) → b
  8. Line(Y_1, Y_2) → d
  9. Line(Y_1, yAxis) → e
  10. Line(Y_2, yAxis) → f
  11. Intersect(b, e) → X_1
  12. Segment(Y_1, X_1) → g
  13. Intersect(b, f) → X_2
  14. Segment(Y_2, X_2) → h_2
  15. OrthogonalLine(Y_1, g) → i
  16. Intersect(i, h_2) → D
  17. Segment(Y_1, D) → j
  18. Ray(Y_1, D) → k
  19. Line(Y_2, b) → l
  20. Point(l) → J
  21. Ray(Y_2, J) → m
  22. Line(K, h_2) → n
  23. Intersect(n, m) → L
  24. Intersect(n, k) → M
  25. Segment(L, M) → ΔY
  26. Point(b) → N
  27. Segment(M, N) → Y
  28. Line(Y_1, yAxis) → r
  29. Line(D, yAxis) → s
  30. Line(O, b) → t
  31. Intersect(r, t) → P
  32. Intersect(s, t) → Q
  33. Segment(P, Q) → ΔX
  34. Intersect(t, yAxis) → R
  35. Segment(R, P) → X
  36. OrthogonalLine(P, X) → p
  37. Point(p) → S
  38. Point(p) → T_1
  39. Ray(Y_1, D) → q
  40. Ray(Y_2, L) → a_1
  41. Ray(Y_1, X_1) → b_1
  42. Ray(Y_2, D) → c_1
  43. Point(c) → E
  44. Point(c) → F
  45. Segment(E, F) → d_1
  46. OrthogonalLine(A, b) → e_1
  47. Point(c) → G
  48. Segment(C, G) → f_1
  49. OrthogonalLine(G, a) → g_1
  50. Intersect(a, g_1) → H
  51. Segment(G, H) → h_1
  52. Intersect(b, d) → T
  53. Segment(T, X_1) → h