MathPlotAI Logo MathPlotAI

Reuleaux Polygons Path Demo

Reuleaux Polygons Path Demo
Loading the math board and drawing, please wait…
2017-07-13 20:06
CirclePolygonTrigonometryComplex NumberGeometric Construction
This example demonstrates the construction and dynamic behavior of Reuleaux polygons and their paths. It involves core mathematical concepts such as polygons, complex numbers, circles, integers, and sine functions. Key GeoGebra commands used include Mod, Vector, Rotate, If, Translate, AngularBisector, Circle, Intersect, Segment, Distance, Line, Mirror, Point, and Polygon. Suitable for high school and above students to understand the geometric properties and path generation of Reuleaux polygons.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a dynamic Reuleaux polygon path demonstration, showing the construction and movement轨迹 of the polygons, involving multiple arcs and line segments, generating complex geometric patterns through rotation and mirror operations, and labeling the positions of key points and paths, reflecting the application of trigonometric functions and complex numbers in geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.