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Lamborghini Turning Angles

Lamborghini Turning Angles
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2023-06-01 22:41
PolygonAngleGeometric Construction
In collections Congruence (Vol 2) Polygons & Angles
This example demonstrates the exterior angle theorem of polygons through geometric construction. Using commands like Polygon, Rotate, Dilate, Vector, and Translate, a polygon is constructed and its exterior angle sum property is illustrated by adjusting the vertex positions. Suitable for students at middle school level and above to learn polygon geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C
  2. Polygon(C, D, 6) → poly1, f, H, g, h, i, j, k, E, F, G
  3. Rotate(pic1, pi / 3, D) → pic1'
  4. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], E) → D'
  5. Vector(D, D') → u
  6. Translate(pic1', u) → pic1''
  7. Ray(D, E) → l
  8. Rotate(pic1'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → pic1'''
  9. Dilate(E, If[2 < a ≤ 3, 3 - a, 0], F) → E'
  10. Vector(E, E') → v
  11. Translate(pic1''', v) → pic2
  12. Rotate(I, pi / 3, D) → I'
  13. Translate(I', u) → I''
  14. Rotate(I'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → I'''
  15. CircleSector(E, I'', I''') → c
  16. Rotate(pic2, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → pic2'
  17. Translate(I''', v) → J
  18. Rotate(J, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → J'
  19. CircleSector(F, J, J') → d
  20. Dilate(E', If[4 < a ≤ 5, 5 - a, 0], G) → E''
  21. Vector(E', E'') → w
  22. Translate(pic2', w) → pic2''
  23. Translate(J', w) → J''
  24. Ray(E, E') → m
  25. Rotate(pic2'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → pic2'''
  26. Rotate(J'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → J'''
  27. CircleSector(G, J'', J''') → e
  28. Ray(E', G) → n
  29. Dilate(G, If[6 < a ≤ 7, 7 - a, 0], H) → G'
  30. Vector(G, G') → b
  31. Translate(pic2''', b) → pic3
  32. Translate(J''', b) → K
  33. Rotate(pic3, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → pic3'
  34. Rotate(K, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → K'
  35. CircleSector(H, K, K') → p
  36. Ray(E'', H) → q
  37. Dilate(H, If[8 < a ≤ 9, 9 - a, 0], C) → H'
  38. Vector(H, H') → r
  39. Translate(pic3', r) → pic3''
  40. Translate(K', r) → K''
  41. Rotate(pic3'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → pic3'''
  42. Rotate(K'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → K'''
  43. CircleSector(C, K'', K''') → s
  44. Ray(H, C) → t
  45. Dilate(C, If[10 < a ≤ 11, 11 - a, 0], D) → C'
  46. Vector(C, C') → u_1
  47. Translate(pic3''', u_1) → pic4
  48. Translate(K''', u_1) → L
  49. Rotate(pic4, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → pic4'
  50. Rotate(L, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → L'
  51. Ray(C, D) → f_1
  52. CircleSector(C', L, L') → c_1
  53. Segment(C, D) → g_1
  54. Segment(D, E) → h_1
  55. Segment(E, F) → i_1
  56. Segment(F, G) → j_1
  57. Segment(G, H) → k_1
  58. Segment(H, C) → l_1
  59. Dilate(C, If[13 < a ≤ 14, 14 - a, 0], M) → C'_{1}
  60. Dilate(H, If[13 < a ≤ 14, 14 - a, 0], M) → H'_{1}
  61. Dilate(G, If[13 < a ≤ 14, 14 - a, 0], M) → G'_{1}
  62. Dilate(F, If[13 < a ≤ 14, 14 - a, 0], M) → F'
  63. Dilate(E, If[13 < a ≤ 14, 14 - a, 0], M) → E'_{1}
  64. Dilate(D, If[13 < a ≤ 14, 14 - a, 0], M) → D'_{1}
  65. Vector(H, H'_{1}) → v_1
  66. Vector(C, C'_{1}) → w_1
  67. Vector(D, D'_{1}) → a_1
  68. Vector(E, E'_{1}) → b_1
  69. Vector(F, F') → d_1
  70. Vector(G, G'_{1}) → e_1
  71. Translate(p, v_1) → p'
  72. Translate(s, w_1) → s'
  73. Translate(c, b_1) → c'
  74. Translate(d, d_1) → d'
  75. Translate(e, e_1) → e'
  76. Translate(c_1, a_1) → p_1
  77. CircleArc(E, I'', I''') → q_1
  78. CircleArc(F, J, J') → r_1
  79. CircleArc(G, J'', J''') → s_1
  80. CircleArc(H, K, K') → t_1
  81. CircleArc(C, K'', K''') → c_2
  82. CircleArc(D, I, I') → d_2

AI Drawing Prompt Reference

In a Cartesian plane, use the intersection point of the x- and y-axes as the base. Construct a regular polygon with 6 vertices using this setup, and obtain its key vertices. Take one polygon vertex as a rotation center and, with a fixed incremental angle, successively rotate and translate the polygon to create a chain of exterior positions that reflect turning between consecutive vertices. At corresponding vertex pairs, draw circular sectors to represent the angles between the rotated rays, illustrating the exterior-angle construction step by step. Finally, draw rays from the relevant outer points back toward the polygon so the sequence of exterior angles is visually connected.
The prompt above was compiled from the original drawing commands and is for reference only.