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Dynamic Dodecagon Demonstration

Dynamic Dodecagon Demonstration
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2018-06-25 06:04
PolygonAngleTransformationGeometric Construction
This example dynamically illustrates the properties and transformations of a regular dodecagon. It involves core mathematical concepts such as polygon construction, angle bisectors, rotations, and similarity transformations. The construction utilizes GeoGebra commands like Polygon, LineBisector, Intersect, Line, Rotate, Segment, Dilate, Midpoint, and Angle. Suitable for high school mathematics education to showcase geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 12) → poly1, f, p, q, r, C, D, E, F, G, H, I, g, J, K, L, h, i, j, k, l, m, n
  2. LineBisector(H, G) → s
  3. LineBisector(G, F) → t
  4. Intersect(s, t) → M
  5. Line(C, K) → b
  6. Line(H, I) → c
  7. Intersect(b, c) → N
  8. Rotate(poly1, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → poly1'
  9. Rotate(A, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → A'
  10. Rotate(B, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → B'
  11. Segment(A', B') → f'
  12. Rotate(B, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → B'_1
  13. Rotate(C, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → C'
  14. Segment(B'_1, C') → g'
  15. Rotate(C, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → C'_1
  16. Rotate(D, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → D'
  17. Segment(C'_1, D') → h'
  18. Rotate(D, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → D'_1
  19. Rotate(E, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → E'
  20. Segment(D'_1, E') → i'
  21. Rotate(E, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → E'_1
  22. Rotate(F, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → F'
  23. Segment(E'_1, F') → j'
  24. Rotate(F, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → F'_1
  25. Rotate(G, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → G'
  26. Segment(F'_1, G') → k'
  27. Rotate(G, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → G'_1
  28. Rotate(H, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → H'
  29. Segment(G'_1, H') → l'
  30. Rotate(H, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → H'_1
  31. Rotate(I, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → I'
  32. Segment(H'_1, I') → m'
  33. Rotate(I, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → I'_1
  34. Rotate(J, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → J'
  35. Segment(I'_1, J') → n'
  36. Rotate(J, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → J'_1
  37. Rotate(K, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → K'
  38. Segment(J'_1, K') → p'
  39. Rotate(K, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → K'_1
  40. Rotate(L, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → L'
  41. Segment(K'_1, L') → q'
  42. Rotate(L, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → L'_1
  43. Rotate(A, If[0 < a ≤ 1, (a * π / 6), π / 6], M) → A'_1
  44. Segment(L'_1, A'_1) → r'
  45. Dilate(C, If[1.5 < a ≤ 2.5, 2.5 - a, 0], K) → C'_2
  46. Segment(C, C'_2) → d
  47. Dilate(K, If[2.5 < a ≤ 3.5, 3.5 - a, 0], N) → K'_2
  48. Dilate(I, If[2.5 < a ≤ 3.5, 3.5 - a, 0], N) → I'_2
  49. Segment(I, I'_2) → e
  50. Segment(K, K'_2) → f_1
  51. Dilate(N, If[4.5 < a ≤ 5.5, 5.5 - a, 0], J) → N'
  52. Segment(N, N') → g_1
  53. Dilate(J, If[5.5 < a ≤ 6.5, 6.5 - a, 0], F) → J'_2
  54. Segment(N', J'_2) → h_1
  55. Segment(N, N') → i_1
  56. Segment(N', J'_2) → j_1
  57. Rotate(F, π / 2, J) → F'_2
  58. Rotate(N', If[7 < a ≤ 8, ((a - 7) * π / 2), π / 2], J) → N''
  59. Rotate(J'_2, If[7 < a ≤ 8, ((a - 7) * π / 2), π / 2], J) → O
  60. Segment(N'', O) → k_1
  61. Midpoint(F'_2, N) → P
  62. Dilate(F'_2, If[8 < a ≤ 9, 9 - a, 0], P) → Q
  63. Segment(F'_2, Q) → l_1
  64. Dilate(P, If[9 < a ≤ 10, 10 - a, 0], N) → P'
  65. Segment(P, P') → m_1
  66. Angle(F'_2, J, N) → α
  67. Rotate(N, If[10 < a ≤ 11, ((a - 10) * π / 3), π / 3], N) → N'_1
  68. Rotate(N', If[10 < a ≤ 11, ((a - 10) * π / 3), π / 3], N) → N''_1
  69. Segment(N'_1, N''_1) → n_1
  70. Rotate(N'_1, If[11 < a ≤ 12, ((a - 11) * π), π], P) → R
  71. Rotate(N''_1, If[11 < a ≤ 12, ((a - 11) * π), π], P) → S
  72. Segment(R, S) → p_1

AI Drawing Prompt Reference

This is a dynamic dodecagon demonstration showing the construction, rotation, and scaling of a regular dodecagon. The figure includes a regular dodecagon, with the rotation center determined by intersecting angle bisectors, then rotating vertices to obtain transformed points, connecting these points with line segments to form a series of segments, and finally scaling some parts. The construction order is: first draw the regular dodecagon, then determine the rotation center, rotate vertices, connect transformed points, and finally scale.
The prompt above was compiled from the original drawing commands and is for reference only.