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Animation 32: Circle and Vector Transformations

Animation 32: Circle and Vector Transformations
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2016-06-17 01:33
CircleVectorTransformation
This example demonstrates the creation of dynamic geometric figures using vector transformations and the properties of circles. Key mathematical concepts include circles, vectors, and geometric transformations. Using GeoGebra commands such as Circle, Vector, Translate, and Rotate, complex geometric shapes can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → a
  3. Point(c) → C
  4. Point(c) → D
  5. Segment(C, D) → d
  6. Point(d) → E
  7. CircleArc(A, C, D) → e
  8. Point(e) → F
  9. CircleArc(A, D, C) → f
  10. Ray(F, E) → b
  11. Intersect(f, b, 1) → G
  12. Segment(F, E) → g
  13. Segment(E, G) → h
  14. Segment(C, E) → i
  15. Segment(E, D) → j
  16. Min(list1) → k
  17. Circle(E, (0.4 * k)) → p
  18. Segment(A, G) → l
  19. Segment(A, C) → m
  20. Segment(A, F) → n
  21. Segment(A, D) → q
  22. Circle(A, (0.4 * k)) → r
  23. Intersect(r, l, 1) → H
  24. Intersect(r, m, 1) → I
  25. Intersect(p, h, 1) → J
  26. Intersect(p, i, 1) → K
  27. Intersect(p, g, 1) → L
  28. Intersect(p, j, 1) → M
  29. Intersect(r, n, 1) → N
  30. Intersect(r, q, 1) → O
  31. Angle(G, A, C) → α
  32. Angle(F, A, D) → β
  33. Rotate(G, (-(α / 2)), A) → G'
  34. Rotate(G, α / 2, A) → G'_1
  35. Angle(G, A, G'_1) → γ
  36. Rotate(F, β / 2, A) → F'
  37. Angle(F, A, F') → δ
  38. Segment(A, F') → s
  39. Segment(A, G'_1) → t
  40. Intersect(r, t, 1) → P
  41. Intersect(r, s, 1) → Q
  42. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], G) → A'
  43. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'_1
  44. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], F) → A'_2
  45. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'_3
  46. Segment(A, A') → a_1
  47. Segment(A, A'_1) → b_1
  48. Segment(A, A'_2) → c_1
  49. Segment(A, A'_3) → d_1
  50. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], G'_1) → A'_4
  51. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], F') → A'_5
  52. Segment(A, A'_4) → e_1
  53. Segment(A, A'_5) → f_1
  54. CircleSector(A, H, P) → g_1
  55. CircleSector(A, N, Q) → h_1
  56. Rotate(g_1, If[2 < o ≤ 3, ((o - 2) * γ), γ], A) → k_1
  57. CircleArc(A, H, P) → p_1
  58. Rotate(h_1, If[3 < o ≤ 4, ((o - 3) * δ), δ], A) → q_1
  59. CircleArc(A, N, Q) → r_1
  60. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], E) → A'_6
  61. Vector(A, A'_6) → u
  62. Translate(k_1, u) → s_1
  63. Translate(I, u) → I'
  64. Angle(I', E, K) → ε
  65. Rotate(s_1, If[5 < o ≤ 6, ((o - 5) * ε), ε], E) → t_1
  66. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], E) → A'_7
  67. Vector(A, A'_7) → v
  68. Translate(q_1, v) → c_2
  69. Angle(J, E, K) → ζ
  70. Translate(P, v) → P'
  71. Rotate(P', ε, E) → P''
  72. Translate(O, v) → O'
  73. Angle(O', E, P'') → η
  74. Rotate(c_2, If[7 < o ≤ 8, ((o - 7) * η), η], E) → d_2
  75. CircleArc(A, F, D) → e_2
  76. CircleArc(A, G, C) → f_2
  77. Intersect(p, h, 1) → R
  78. CircleSector(E, R, K) → g_2