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雨刮器与数学模型

雨刮器与数学模型
几何画板及绘图内容加载中，请稍等……
2020-01-14 23:59
圆角向量解析几何微积分
①本范例通过雨刮器运动演示抛物线与圆的交点及角度变化；②涉及核心数学概念包括角度、抛物线、解析几何、微积分中的求和与极限；③作图要点提炼自构造摘要，使用了Circle, Point, Segment, Line, Ray, Intersect, Angle, Vector, Midpoint, Mirror等命令与对象；④适合高中及以上学生，用于理解几何作图与微积分应用。

GeoGebra 命令及参数

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Point(Circle[B, 4]) → C
  4. Segment(B, C) → f
  5. Line(C, f_1) → g
  6. Line(D, f_1) → h
  7. Ray(C, D) → i
  8. Point(h) → E
  9. Line(E, i) → j
  10. Intersect(g, j) → F
  11. Circle(D, 5) → d
  12. Intersect(d, i, 1) → G
  13. Line(G, h) → k
  14. Intersect(j, k) → H
  15. Point(h) → I
  16. Angle(G, D, I) → α
  17. Angle(H, E, I) → β
  18. Segment(G, D) → n
  19. Segment(H, E) → p
  20. Vector(J, K) → u
  21. Intersect(i, h) → C_1
  22. Intersect(i, n) → D_1
  23. Intersect(i, n) → E_1
  24. Intersect(h, f) → F_1
  25. Midpoint(C, F) → L
  26. Midpoint(G, H) → O
  27. Line(L, O) → l
  28. Point(Circle[C, 0.5]) → Q
  29. Segment(C, Q) → m
  30. Line(Q, i) → q
  31. Mirror(q, l) → q'
  32. Point(l) → P
  33. Line(P, g) → s
  34. Intersect(q, s) → R
  35. Intersect(q', s) → S
  36. Intersect(h, q') → T
  37. Intersect(h, q) → U
  38. Intersect(j, s) → V
  39. Intersect(s, i) → W
  40. Mirror(q, i) → q'_{1}
  41. Intersect(q'_{1}, s) → Z
  42. Intersect(q'_{1}, h) → A_1
  43. Mirror(q', p) → q''
  44. Intersect(q'', s) → B_1
  45. Segment(W, D) → t
  46. Segment(V, E) → a