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摩天轮模型

摩天轮模型
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2017-06-13 02:30
角函数三角函数几何作图
所属专题 Math Year 4 Unit 1
①本范例通过动态演示摩天轮的运动，展示角度、正弦函数与指数函数的关联；②涉及核心数学概念包括角度测量、三角函数应用、等腰与等边三角形特性、指数运算；③作图要点运用了Circle（圆）、Segment（线段）、Rotate（旋转）、Angle（角度）、Line（直线）、OrthogonalLine（垂线）、Intersect（交点）、Distance（距离）等GeoGebra命令；④适合高中数学教学，用于理解函数模型与几何变换的结合应用。

GeoGebra 命令及参数

  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. Segment(Zero'_1, B) → a_1
  47. Angle(Zero'_1, B, C) → ξ
  48. Angle(B, C, Zero'_1) → ο
  49. OrthogonalLine(Zero'_2, d) → b_1
  50. Intersect(b_1, d) → D
  51. Segment(Zero'_2, D) → c_1
  52. Distance(D, C) → distanceDC
  53. Angle(D, C, Zero'_2) → ρ
  54. Angle(Zero'_2, D, C) → σ