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Windshield Wipers Math Model

Windshield Wipers Math Model
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2020-01-14 23:59
CircleAngleVectorCoordinate GeometryCalculus
This example demonstrates the intersection of parabolas and circles through the motion of windshield wipers, involving core math concepts like angles, parabolas, coordinate geometry, and calculus concepts such as sums and limits. Construction highlights include commands like Circle, Point, Segment, Line, Ray, Intersect, Angle, Vector, Midpoint, Mirror as per the GeoGebra summary. Ideal for high school and above to explore geometric constructions and calculus applications.

GeoGebra Commands & Parameters

  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