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Animation 278: Polygons and Transformations

Animation 278: Polygons and Transformations
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2017-06-03 09:01
PolygonVectorFunctionTransformationGeometric Construction
This example demonstrates polygon rotation, dilation, and locus changes through animation; core concepts include polygon construction, angle transformations, vector operations, quadratic functions, and fractal geometry; constructed using commands like Polygon, Rotate, Dilate, Vector, Translate; suitable for high school and above to explore geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. Rotate(B, 144°, C) → B'
  3. Ray(C, B') → s
  4. Line(B, C) → k
  5. Circle(C, a) → c
  6. Intersect(c, s) → N,
  7. Intersect(c, k) → F, G
  8. CircleArc(C, F, N) → e
  9. Line(C, D) → l
  10. Intersect(c, l) → H, I
  11. CircleArc(C, F, I) → d
  12. Point(e) → J
  13. Polygon(C, J, 5) → poly2, m, n, p, q, r, K, L, M
  14. Angle(B, C, B') → α
  15. Segment(D, A) → t
  16. Segment(D, B) → b
  17. LineBisector(D, C) → f_1
  18. LineBisector(B, C) → g_1
  19. LineBisector(M, L) → h_1
  20. LineBisector(L, K) → i_1
  21. Segment(M, J) → j_1
  22. Segment(E, K) → k_1
  23. Segment(A, L) → l_1
  24. Intersect(k_1, l_1) → Q
  25. Circle(D, (0.2 * j_1)) → c_1
  26. Segment(D, E) → m_1
  27. Intersect(c_1, t, 1) → R
  28. Intersect(i, m_1) → S
  29. Intersect(c_1, m_1) → T,
  30. CircleSector(D, T, R) → d_1
  31. Dilate(E, If[0 < o ≤ 1, 1 - o, 0], K) → E'
  32. Segment(E, E') → n_1
  33. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], Q) → A'
  34. Segment(A, A') → p_1
  35. Dilate(Q, If[2 < o ≤ 3, 3 - o, 0], L) → Q'
  36. Segment(Q, Q') → q_1
  37. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], A) → D'
  38. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'_1
  39. Segment(D, D') → r_1
  40. Segment(D, D'_1) → s_1
  41. Rotate(d_1, If[5 < o ≤ 6, (((o - 5) * 36) * π / 180), (36 * π / 180)], D) → e_1
  42. Rotate(e_1, If[7 < o ≤ 8, (((o - 7) * 36) * π / 180), (36 * π / 180)], D) → t_1
  43. Line(Q, s_1) → a_1
  44. Dilate(D, If[9 < o ≤ 10, 10 - o, 0], Q) → D'_2
  45. Vector(D, D'_2) → u
  46. Translate(t_1, u) → c_2
  47. Segment(D, E) → b_1
  48. Segment(E, A) → f_2
  49. Segment(A, B) → g_2
  50. Segment(B, C) → h_2
  51. Segment(C, D) → i_2
  52. Segment(C, M) → j_2
  53. Segment(M, L) → k_2
  54. Segment(L, K) → l_2
  55. Segment(K, J) → m_2
  56. Segment(J, C) → n_2
  57. Point(a_1) → O
  58. Angle(O, Q, K) → β
  59. Rotate(c_2, If[10 < o ≤ 11, ((o - 10) * β), β], Q) → d_2