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Shearer Dynamic Geometry Demo

Shearer Dynamic Geometry Demo
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2019-12-16 23:52
PolygonVectorTransformationGeometric Construction
This example dynamically illustrates a geometric transformation problem posted by Catriona Shearer, involving core math concepts like rectangles, algebra, binomial distribution, LCM and GCD, quadrilaterals, and combinatorics. It is constructed using GeoGebra commands such as Intersect, Rotate, Ray, OrthogonalLine, Polygon, Distance, Circle, Segment, Angle, Dilate, Vector, Translate, and CircleSector, making it suitable for high school and above learners to explore complex geometric constructions and dynamic changes.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Rotate(F, (-(15°)), A) → F'_1
  3. Ray(A, F'_1) → f
  4. OrthogonalLine(F'_1, yAxis) → g
  5. Intersect(g, yAxis) → H
  6. OrthogonalLine(D, yAxis) → h
  7. Intersect(h, yAxis) → I
  8. Polygon(A, B, D, I) → q1, a_1, b_1, d, i
  9. Distance(A, F'_1) → c
  10. Circle(D, Distance[D, B]) → e
  11. Segment(H, A) → q
  12. Segment(A, B) → r
  13. Segment(H, F'_1) → s
  14. Segment(F'_1, E) → t
  15. Segment(I, D) → f_1
  16. Segment(D, B) → g_1
  17. Segment(A, D) → j
  18. Polygon(A, D, 3) → poly1, k, l, m, C
  19. Circle(D, s) → p
  20. Rotate(D, (-(15°)), C) → D'
  21. Rotate(D, 75°, C) → D'_1
  22. Segment(F'_1, D'_1) → n
  23. Ray(F'_1, D') → b
  24. OrthogonalLine(D, b) → h_1
  25. Intersect(h_1, b) → J
  26. OrthogonalLine(D, h_1) → i_1
  27. Intersect(i_1, n) → K
  28. Segment(F'_1, J) → j_1
  29. Segment(J, D) → k_1
  30. Segment(D, K) → l_1
  31. Segment(K, F'_1) → m_1
  32. Angle(K, F'_1, H) → α
  33. Angle(j_1, f_1) → β
  34. Rotate(A, If[0 < o ≤ 1, ((-o) * π / 3), ((-π)) / 3], D) → A'
  35. Rotate(B, If[0 < o ≤ 1, ((-o) * π / 3), ((-π)) / 3], D) → B'
  36. Rotate(D, If[0 < o ≤ 1, ((-o) * π / 3), ((-π)) / 3], D) → D'_2
  37. Rotate(I, If[0 < o ≤ 1, ((-o) * π / 3), ((-π)) / 3], D) → I'
  38. Polygon(A', B', D'_2, I') → q1', a', b', d'_2, i'
  39. Dilate(J, If[2 < o ≤ 3, 3 - o, 0], A) → J'
  40. Vector(J, J') → u
  41. Translate(A', u) → A''
  42. Translate(B', u) → B''
  43. Translate(D'_2, u) → G
  44. Translate(I', u) → I''
  45. Polygon(A'', B'', G, I'') → q1'', a'', b'', g_2, i''
  46. Rotate(A'', If[2 < o ≤ 3, ((-(o - 2)) * π / 6), ((-π)) / 6], B'') → A'''
  47. Rotate(B'', If[2 < o ≤ 3, ((-(o - 2)) * π / 6), ((-π)) / 6], B'') → B'''
  48. Rotate(G, If[2 < o ≤ 3, ((-(o - 2)) * π / 6), ((-π)) / 6], B'') → G'
  49. Rotate(I'', If[2 < o ≤ 3, ((-(o - 2)) * π / 6), ((-π)) / 6], B'') → I'''
  50. Polygon(A''', B''', G', I''') → q1''', a''', b''', g', i'''
  51. Angle(B, A, H) → γ
  52. Angle(A, I, D) → δ
  53. Angle(J, F'_1, K) → ε
  54. Angle(I, H, F'_1) → ζ
  55. Angle(F'_1, K, D) → η
  56. Angle(D, B, A) → θ
  57. Angle(D, J, F'_1) → ι
  58. Intersect(f_1, j_1) → L
  59. Intersect(t, f_1) → M
  60. Circle(L, Distance[M, L] / 2) → c_1
  61. Angle(F'_1, E, A) → κ
  62. Intersect(c_1, f_1, 1) → N
  63. Rotate(N, ((-π)) / 6, L) → N'
  64. Ray(L, N') → n_1
  65. Circle(L, (2 * Radius[c_1])) → d_1
  66. Intersect(d_1, n_1, 1) → O
  67. Dilate(L, If[4 < o ≤ 5, 5 - o, 0], O) → L'
  68. Rotate(N, If[4 < o ≤ 5, ((-(o - 4)) * π / 6), ((-π)) / 6], L) → N'_1
  69. Segment(L, L') → p_1
  70. CircleSector(L, N'_1, N) → e_1
  71. Rotate(e_1, If[6 < o ≤ 7, ((-(o - 6)) * π / 6), ((-π)) / 6], L) → q_1
  72. Dilate(L, If[8 < o ≤ 9, 9 - o, 0], C) → L'_1
  73. Vector(L, L'_1) → v
  74. Translate(q_1, v) → r_1
  75. Rotate(r_1, If[8 < o ≤ 9, (((o - 8) * 5) * π / 6), (5 * π / 6)], L'_1) → s_1