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Dynamic Geometric Illustration by Tim Brzezinski

Dynamic Geometric Illustration by Tim Brzezinski
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2018-04-22 03:19
PolygonVectorFunctionTrigonometryGeometric Construction
This example demonstrates a dynamic and modifiable illustration of a problem posted by Antonio Gutierrez on Twitter. It involves core mathematical concepts such as square, polynomial functions, fractal geometry, addition, unit circle, and division. Construction highlights include using commands and objects like Segment, Rotate, Angle, Ray, Point, Polygon, Midpoint, Line, Dilate, Vector, Translate, Intersect, Min, Circle, and CircleSector. Suitable for high school students and enthusiasts to explore and visualize complex geometric and algebraic relationships.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(C, B) → h
  7. Segment(A, C) → i
  8. Polygon(B, A, 4) → poly1, j, k, l, m, D, E
  9. Polygon(E, D, 4) → poly2, n, p, q, r, F, G
  10. Polygon(A, C, 4) → poly3, s, t, b, c, H, I
  11. Polygon(C, B, 4) → poly4, d, e, f_1, g_1, J, K
  12. Polygon(A, B, C) → t1, c_1, a_1, b_1
  13. Midpoint(F, E) → L
  14. Line(L, C) → h_1
  15. Line(D, K) → i_1
  16. Line(E, H) → j_1
  17. Angle(B, C, K) → β
  18. Angle(C, K, J) → γ
  19. Angle(K, J, B) → δ
  20. Angle(A, I, H) → ε
  21. Angle(I, H, C) → ζ
  22. Angle(C, A, I) → η
  23. Angle(A, B, E) → θ
  24. Angle(B, E, D) → ι
  25. Angle(E, D, A) → κ
  26. Rotate(C, If[0 < o ≤ 1, (o * π / 2), π / 2], C) → C'
  27. Rotate(B, If[0 < o ≤ 1, (o * π / 2), π / 2], C) → B'_1
  28. Segment(C', B'_1) → h'
  29. Rotate(A, If[0 < o ≤ 1, (o * π / 2), π / 2], A) → A'
  30. Rotate(C, If[0 < o ≤ 1, (o * π / 2), π / 2], A) → C'_1
  31. Segment(A', C'_1) → i'
  32. Rotate(A, If[0 < o ≤ 1, (o * π / 2), π / 2], B) → A'_1
  33. Rotate(B, If[0 < o ≤ 1, (o * π / 2), π / 2], B) → B'_2
  34. Segment(A'_1, B'_2) → f'
  35. Rotate(C', If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], K) → C''
  36. Rotate(B'_1, If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], K) → M
  37. Segment(C'', M) → h''
  38. Rotate(A', If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], I) → A''
  39. Rotate(C'_1, If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], I) → N
  40. Segment(A'', N) → i''
  41. Rotate(A'_1, If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], E) → O
  42. Rotate(B'_2, If[1 < o ≤ 2, ((o - 1) * π / 2), π / 2], E) → P
  43. Segment(O, P) → f''
  44. Rotate(C'', If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], J) → C'''
  45. Rotate(M, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], J) → M'
  46. Segment(C''', M') → h'''
  47. Rotate(O, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], D) → O'
  48. Rotate(P, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], D) → P'
  49. Segment(O', P') → f'''
  50. Rotate(A'', If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], H) → A'''
  51. Rotate(N, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], H) → N'
  52. Segment(A''', N') → i'''
  53. Rotate(O, If[4 < o ≤ 5, ((o - 4) * π / 2), π / 2], E) → O'_1
  54. Rotate(P, If[4 < o ≤ 5, ((o - 4) * π / 2), π / 2], E) → P'_1
  55. Segment(O'_1, P'_1) → f'''_1
  56. Dilate(E, If[5 < o ≤ 6, 6 - o, 0], D) → E'
  57. Vector(E, E') → u
  58. Translate(O'_1, u) → Q
  59. Translate(P'_1, u) → R
  60. Segment(Q, R) → k_1
  61. Dilate(D, If[6 < o ≤ 7, 7 - o, 0], F) → D'
  62. Vector(D, D') → v
  63. Translate(O, v) → O'_2
  64. Translate(P, v) → P'_2
  65. Segment(O'_2, P'_2) → f'''_2
  66. Dilate(F, If[7 < o ≤ 8, 8 - o, 0], L) → F'
  67. Segment(F, F') → l_1
  68. Dilate(L, If[8 < o ≤ 9, 9 - o, 0], E) → L'
  69. Segment(L, L') → m_1
  70. Rotate(F, If[9 < o ≤ 10, ((o - 9) * π), π], L) → F'_1
  71. Rotate(F', If[9 < o ≤ 10, ((o - 9) * π), π], L) → F''
  72. Segment(F'_1, F'') → n_1
  73. Intersect(h_1, j_1) → S
  74. Dilate(L, If[11 < o ≤ 12, 12 - o, 0], C) → L'_1
  75. Segment(L, L'_1) → p_1
  76. Dilate(H, If[12 < o ≤ 13, 13 - o, 0], S) → H'
  77. Segment(H, H') → q_1
  78. Dilate(S, If[13 < o ≤ 14, 14 - o, 0], E) → S'
  79. Segment(S, S') → r_1
  80. Dilate(K, If[14 < o ≤ 15, 15 - o, 0], S) → K'
  81. Segment(K, K') → s_1
  82. Intersect(h_1, j_1) → T
  83. Dilate(S, If[15 < o ≤ 16, 16 - o, 0], D) → S'_1
  84. Segment(S, S'_1) → t_1
  85. Min(f, i) → w
  86. Circle(A, (0.3 * w)) → d_1
  87. Intersect(d_1, f) → U,
  88. Intersect(d_1, i) → V,
  89. CircleSector(A, U, V) → e_1

AI Drawing Prompt Reference

Draw a dynamic geometric illustration featuring a square and four surrounding regular quadrilaterals that rotate around a central point. A line segment extends from the center to one corner of the square, forming a ray upon rotation. A point is placed at the end of the ray, connected to the opposite corner of the square by two line segments. Angle measurements are marked between the shapes, showing their relationships. The entire figure can be dynamically rotated to visualize geometric and algebraic concepts.
The prompt above was compiled from the original drawing commands and is for reference only.