等距多边形路径演示

等距多边形路径演示
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2017-07-13 20:06
①本范例演示了等距多边形及其路径的构造与动态变化;②涉及的核心数学概念包括多边形、复数、圆、整数、正弦函数等;③作图要点提炼自 GeoGebra 命令:Mod(模运算)、Vector(向量)、Rotate(旋转)、If(条件判断)、Translate(平移)、AngularBisector(角平分线)、Circle(画圆)、Intersect(交点)、Segment(线段)、Distance(距离)、Line(直线)、Mirror(镜像)、Point(点)、Polygon(多边形);④适合高中及以上数学学习者,用于理解等距多边形的几何性质和路径生成。

GeoGebra 命令及参数

  1. Mod(t, 0.62832) → tm
  2. Mod(t, 1.0472) → tmod1
  3. Mod(t, 2.0944) → tmod2
  4. Mod(t, 0.62832) → tmod3
  5. Mod(t, 1.25664) → tmod4
  6. Vector((0, 0), (-12.56637, 0)) → u
  7. Rotate(A1, (-tmod1), A2) → B1
  8. Rotate(A2, (-tmod1), A1) → B2
  9. Rotate(A3, (-tmod1), A1) → B3
  10. Rotate(A4, (-tmod1), A2) → B4
  11. If(flag1, CircleArc[A1, B2, B3], CircleArc[A2, B1, B4]) → C1
  12. If(flag1, CircleArc[B3, A1, B2], CircleArc[B4, A2, B1]) → C2
  13. If(flag1, CircleArc[B2, B3, A1], CircleArc[B1, B4, A2]) → C3
  14. If(flag1, Polygon[A1, B2, B3], Polygon[A2, B1, B4]) → C4
  15. Translate(C1, u) → D1
  16. Translate(C2, u) → D2
  17. Translate(C3, u) → D3
  18. Translate(C4, u) → D4
  19. AngularBisector(B1, A2, B4) → e
  20. AngularBisector(A2, B4, B1) → f
  21. AngularBisector(B3, B2, A1) → g
  22. AngularBisector(B2, A1, B3) → h
  23. If(flag1, Intersect[g, h], Intersect[e, f]) → A
  24. Translate(A, u) → A'
  25. Circle(C, radius) → c
  26. Translate(C, u) → C'
  27. Translate(c, u) → c'
  28. Intersect(c, xAxis, 2) → F
  29. Rotate(F, (-t), C) → F'
  30. Rotate(F, π - t, C) → F_1'
  31. Segment(F_1', F') → d
  32. Translate(F_1', u) → G
  33. Translate(F', u) → F''
  34. Segment(G, F'') → d'
  35. Distance(A8, A7) → di1
  36. Rotate(A7, -1.8849555921538759, A8) → A9
  37. Rotate(A8, -1.88495559215388, A9) → A10
  38. Rotate(A9, -1.88495559215388, A10) → A11
  39. Line(A11, A9) → l
  40. Mirror(A10, l) → A12
  41. Mirror(A7, l) → A13
  42. Mirror(A8, l) → A14
  43. Rotate(A7, (-tm), $A$9) → B7
  44. Rotate(A8, (-tm), $A$9) → B8
  45. Rotate(A10, (-tm), $A$9) → B10
  46. Rotate(A11, (-tm), $A$9) → B11
  47. Rotate(A9, (-tm), $A$11) → C9
  48. Rotate(A12, (-tm), $A$11) → C12
  49. Rotate(A13, (-tm), $A$11) → C13
  50. Rotate(A14, (-tm), $A$11) → C14
  51. If(flag2, CircleArc[A9, B11, B7], CircleArc[A11, C9, C14]) → D7
  52. If(flag2, CircleArc[B8, B10, B11], CircleArc[C13, C12, C9]) → D8
  53. If(flag2, CircleArc[B7, A9, B10], CircleArc[C14, A11, C12]) → D9
  54. If(flag2, CircleArc[B11, B8, A9], CircleArc[C9, C13, A11]) → D10
  55. If(flag2, CircleArc[B10, B7, B8], CircleArc[C12, C14, C13]) → D11
  56. If(flag2, Polygon[B10, B11, 5], Polygon[C14, C13, 5]) → D12
  57. Translate(D7, u) → E7
  58. Translate(D8, u) → E8
  59. Translate(D9, u) → E9
  60. Translate(D10, u) → E10
  61. Translate(D11, u) → E11
  62. Translate(D12, u) → E12
  63. AngularBisector(C13, C14, C9) → m
  64. AngularBisector(C14, C9, C12) → n
  65. AngularBisector(B8, B7, B11) → p
  66. AngularBisector(B7, B11, B10) → q
  67. If(flag2, Intersect[p, q], Intersect[m, n]) → B
  68. Point(b) → D
  69. Point(b) → E
  70. Polygon(D, E, 4) → poly1, i, j, k, r, H, I
  71. Point(a) → J
  72. Point(a) → K
  73. Polygon(J, K, 4) → poly2, s, a_1, b_1, c_1, L, M
  74. Translate(B, u) → B'

AI 绘图提示语参考

绘制一个动态的雷奥劳斯多边形路径演示,展示多边形的构造和运动轨迹,包含多个圆弧和折线段,通过旋转和镜像操作生成复杂的几何图案,并标注关键点的位置和路径,体现三角函数和复数在几何构造中的应用。
以上提示语为根据原始绘图命令整理而来,仅供参考。