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AB Ferris Wheel 09 - Dive into Moving Cart

AB Ferris Wheel 09 - Dive into Moving Cart
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2017-06-15 05:00
CircleTrigonometryCoordinate GeometryGeometric Construction
In collections Math Year 4 Unit 1
This example demonstrates the trajectory of a moving cart on a Ferris wheel and its related geometric properties. Core math concepts include circle, triangle, angle, and linear regression. Construction highlights involve commands like Circle, Segment, Rotate, Angle, Line, OrthogonalLine, Intersect, and Distance from GeoGebra, suitable for high school students learning analytical geometry, solid geometry, and parametric equations.

GeoGebra Commands & Parameters

  1. Circle(C, 50) → c
  2. Segment(C, G1) → a
  3. Segment(C, G2) → b
  4. Rotate(Zero, α, C) → Zero'
  5. Angle(Zero, C, Zero') → β
  6. Segment(C, Zero') → d
  7. Rotate(Zero, 30° + α, C) → Zero'_1
  8. Angle(Zero, C, Zero'_1) → γ
  9. Segment(C, Zero'_1) → e
  10. Rotate(Zero, 60° + α, C) → Zero'_2
  11. Angle(Zero, C, Zero'_2) → δ
  12. Segment(C, Zero'_2) → f
  13. Rotate(Zero, 90° + α, C) → Zero'_3
  14. Angle(Zero, C, Zero'_3) → ε
  15. Segment(Zero'_3, C) → g
  16. Rotate(Zero, 120° + α, C) → Zero'_4
  17. Angle(Zero, C, Zero'_4) → ζ
  18. Segment(Zero'_4, C) → h
  19. Rotate(Zero, 150° + α, C) → Zero'_5
  20. Angle(Zero, C, Zero'_5) → η
  21. Segment(Zero'_5, C) → i
  22. Rotate(Zero, 180° + α, C) → Zero'_6
  23. Angle(Zero, C, Zero'_6) → θ
  24. Segment(Zero'_6, C) → j
  25. Rotate(Zero, 210° + α, C) → Zero'_7
  26. Angle(Zero, C, Zero'_7) → ι
  27. Segment(Zero'_7, C) → k
  28. Rotate(Zero, 240° + α, C) → Zero'_8
  29. Angle(Zero, C, Zero'_8) → κ
  30. Segment(Zero'_8, C) → l
  31. Rotate(Zero, 270° + α, C) → Zero'_9
  32. Angle(Zero, C, Zero'_9) → λ
  33. Segment(Zero'_9, C) → m
  34. Rotate(Zero, 300° + α, C) → Zero'_{10}
  35. Angle(Zero, C, Zero'_{10}) → μ
  36. Segment(Zero'_{10}, C) → n
  37. Rotate(Zero, 330° + α, C) → Zero'_{11}
  38. Angle(Zero, C, Zero'_{11}) → ν
  39. Segment(Zero'_{11}, C) → p
  40. Line(G1, G2) → q
  41. OrthogonalLine(Zero', q) → r
  42. Intersect(r, q) → A
  43. Segment(Zero', A) → s
  44. OrthogonalLine(Zero'_1, d) → t
  45. Intersect(d, t) → B
  46. OrthogonalLine(Zero'_2, d) → b_1
  47. Intersect(b_1, d) → D
  48. Distance(D, C) → distanceDC
  49. Intersect(f_1, g_1, (12.282854594082735, -17.547711629319735)) → E