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Dynamic Illustration of Relationship Between Regular Pentagon and Decagon

Dynamic Illustration of Relationship Between Regular Pentagon and Decagon
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2017-03-10 06:38
PolygonAngleTransformation
In collections Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles
This example dynamically illustrates the relationship between a regular pentagon and a regular decagon. It involves key mathematical concepts such as angles, polygons, and geometric transformations. Using GeoGebra commands like Polygon, Segment, Intersect, etc., it provides a clear understanding of the transformations and relationships between these geometric shapes. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. Polygon(C, B, 10) → poly2, k, a, F, G, H, I, J, K, L, M, l, m, n, p, q, r, s, t
  3. Segment(F, G) → b
  4. Segment(G, H) → c
  5. Segment(H, I) → d
  6. Segment(I, J) → e
  7. Segment(J, K) → f_1
  8. Segment(K, L) → g_1
  9. Segment(L, M) → h_1
  10. Segment(M, C) → i_1
  11. Segment(C, B) → j_1
  12. Segment(B, F) → k_1
  13. Segment(B, A) → l_1
  14. Segment(A, E) → m_1
  15. Segment(E, D) → n_1
  16. Segment(D, C) → p_1
  17. Segment(D, K) → r_1
  18. Segment(A, L) → q_1
  19. Intersect(r_1, q_1) → N
  20. Segment(E, B) → s_1
  21. Segment(E, C) → t_1
  22. Circle(E, (0.35 * n_1)) → c_1
  23. Intersect(c_1, n_1, 1) → O
  24. Intersect(c_1, t_1, 1) → P
  25. Intersect(c_1, s_1, 1) → Q
  26. Intersect(c_1, m_1, 1) → R
  27. CircleSector(E, R, Q) → d_1
  28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], N) → A'
  29. Segment(A, A') → a_1
  30. Dilate(N, If[1 < o ≤ 2, 2 - o, 0], L) → N'
  31. Segment(N, N') → b_1
  32. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], N) → D'
  33. Segment(D, D') → e_1
  34. Dilate(N, If[3 < o ≤ 4, 4 - o, 0], K) → N'_1
  35. Segment(N, N'_1) → f_2
  36. Dilate(E, If[4 < o ≤ 5, 5 - o, 0], B) → E'
  37. Segment(E, E') → g_2
  38. Dilate(E, If[5 < o ≤ 6, 6 - o, 0], C) → E'_1
  39. Segment(E, E'_1) → h_2
  40. Rotate(d_1, If[7 < o ≤ 8, (((o - 7) * 36) * π / 180), (36 * π / 180)], E) → c_2
  41. Rotate(c_2, If[8.5 < o ≤ 9.5, (((o - 8.5) * 36) * π / 180), (36 * π / 180)], E) → d_2
  42. Line(N, n_1) → i_2
  43. Line(E, a_1) → j_2
  44. Dilate(E, If[10 < o ≤ 11, 11 - o, 0], N) → E'_2
  45. Vector(E, E'_2) → u
  46. Translate(d_2, u) → e_2
  47. Point(i_2) → T
  48. Angle(A, N, T) → α
  49. Rotate(e_2, If[11 < o ≤ 12, ((o - 11) * (π - α)), π - α], N) → k_2