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鹦鹉螺的等比生长

鹦鹉螺的等比生长
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2016-12-02 04:50
角向量复数变换参数方程
所属专题 Logarithmic Spiral and Fibonacci Numbers
这个范例演示了鹦鹉螺壳的等比生长过程。涉及的核心数学概念包括相似变换、向量、参数曲线和复数。通过使用GeoGebra命令如Segment、Rotate、Angle、Ray、Circle、Intersect、Polygon等，可以构造出鹦鹉螺壳的生长轨迹。适合高中数学教学和研究。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Rotate(A, (-δ), B) → A'
  3. Angle(A', B, A) → α
  4. Rotate(B, ζ, A) → B'
  5. Angle(B, A, B') → β
  6. Ray(A, B') → g
  7. Ray(B, A') → h
  8. Circle(A, a) → c_2
  9. Intersect(c_2, g) → D,
  10. Circle(B, b) → d_1
  11. Intersect(d_1, h) → C,
  12. Rotate(C, β, D) → C'
  13. Ray(D, C') → j
  14. Polygon(A1) → C1
  15. Rotate(D, (-α), C) → D'
  16. Angle(D', C, D) → γ
  17. Rotate(C, β, D) → C'_1
  18. Angle(C, D, C'_1) → ε
  19. Ray(C, D') → i
  20. Ray(D, C'_1) → k
  21. Circle(C, (Distance[B, C] * B1)) → c
  22. Circle(D, (Distance[A, D] * B1)) → d
  23. Polygon(A2) → C2
  24. Polygon(A3) → C3
  25. Polygon(A4) → C4
  26. Polygon(A5) → C5
  27. Polygon(A6) → C6
  28. Polygon(A7) → C7
  29. Polygon(A8) → C8
  30. Polygon(A9) → C9
  31. Polygon(A10) → C10
  32. Polygon(A11) → C11
  33. Polygon(A12) → C12
  34. Polygon(A13) → C13
  35. Polygon(A14) → C14
  36. Polygon(A15) → C15
  37. Polygon(A16) → C16
  38. Polygon(A17) → C17
  39. Polygon(A18) → C18
  40. Polygon(A19) → C19
  41. Polygon(A20) → C20
  42. Polygon(A21) → C21
  43. Polygon(A22) → C22
  44. Polygon(A23) → C23
  45. Polygon(A24) → C24
  46. Polygon(A25) → C25
  47. Polygon(A26) → C26
  48. Polygon(A27) → C27
  49. Polygon(A28) → C28
  50. Polygon(A29) → C29
  51. Polygon(A30) → C30
  52. Polygon(A31) → C31
  53. Polygon(A32) → C32
  54. Polygon(A33) → C33
  55. Polygon(A34) → C34
  56. Polygon(A35) → C35
  57. Polygon(A36) → C36