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Dynamic Geometry Illustration by Tim Brzezinski (6)

Dynamic Geometry Illustration by Tim Brzezinski (6)
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2019-01-14 21:33
PolygonAngleVectorTrigonometryGeometric Construction
This example dynamically demonstrates a geometry problem posed by Antonio Gutierrez, showcasing geometric relationships through adjustable illustrations. Core mathematical concepts involved include trigonometry, rational numbers, congruence, intersection, addition, etc. Construction highlights utilize GeoGebra commands and objects such as Rotate, Angle, Ray, Point, Intersect, Segment, Polygon, OrthogonalLine, Circle, CircleSector, Semicircle, Midpoint, Vector, Translate, Line, Dilate, and CircleArc. Suitable for high school and above, for geometric construction and concept comprehension.

GeoGebra Commands & Parameters

  1. Rotate(A, atan(1 / 3), B) → A'
  2. Angle(A, B, A') → β
  3. Ray(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Rotate(B, π / 2 + β, C) → B'
  7. Angle(B, C, B') → γ
  8. Ray(C, B') → h
  9. Intersect(h, f) → D
  10. Segment(B, C) → i
  11. Segment(C, D) → j
  12. Polygon(B, D, C) → t1, c, b, d
  13. OrthogonalLine(B, f) → k
  14. Point(k) → E
  15. Angle(E, B, D) → α
  16. Rotate(B, 90°, C) → B'_1
  17. Ray(C, B'_1) → l
  18. Intersect(f, l) → F
  19. Circle(B, (0.5 * j)) → e
  20. Intersect(e, k, 1) → G
  21. Rotate(G, If[0 < m ≤ 1, (m * (π / 2 + β)), π / 2 + β], B) → G'
  22. CircleSector(B, G, G') → p
  23. Semicircle(C, B) → q
  24. Midpoint(i) → H
  25. Rotate(B, If[2 < m ≤ 3, ((m - 2) * π), π], H) → B'_2
  26. Vector(B, B'_2) → u
  27. Translate(p, u) → p'
  28. Line(C, k) → n
  29. Point(n) → I
  30. Angle(B, C, I) → δ
  31. Rotate(p', If[2 < m ≤ 3, ((-(m - 2)) * δ), (-δ)], B'_2) → p''
  32. Angle(C, D, B) → ε
  33. Rotate(C, If[4 < m ≤ 5, ((m - 4) * ε), ε], D) → C'
  34. Rotate(D, If[4 < m ≤ 5, ((m - 4) * ε), ε], D) → D'
  35. Segment(C', D') → j'
  36. Rotate(C', If[5 < m ≤ 6, ((m - 5) * π), π], C') → C''
  37. Rotate(D', If[5 < m ≤ 6, ((m - 5) * π), π], C') → D''
  38. Segment(C'', D'') → j''
  39. Rotate(C'', If[6 < m ≤ 7, ((m - 6) * π), π], D'') → C'''
  40. Rotate(D'', If[6 < m ≤ 7, ((m - 6) * π), π], D'') → D'''
  41. Segment(C''', D''') → j'''
  42. Intersect(e, k, 1) → J
  43. Ray(C, B) → r
  44. Intersect(e, r, 2) → K
  45. Rotate(C''', If[8 < m ≤ 9, ((-(m - 8)) * π / 2), ((-π)) / 2], B) → L
  46. Rotate(D''', If[8 < m ≤ 9, ((-(m - 8)) * π / 2), ((-π)) / 2], B) → M
  47. Segment(L, M) → s
  48. Dilate(M, If[9 < m ≤ 10, 10 - m, 0], D) → M'
  49. Segment(M, M') → t
  50. Polygon(B, M, D) → t2, d_1, b_1, m_1
  51. Circle(D, (0.5 * j)) → c_1
  52. Intersect(c_1, j') → N,
  53. Rotate(N, If[11 < m ≤ 12, ((m - 11) * β), β], D) → N'
  54. CircleSector(D, N, N') → e_1
  55. Intersect(c_1, t) → O,
  56. Circle(B, (0.4 * i)) → f_1
  57. Intersect(f_1, i) → P,
  58. Dilate(D, If[13 < m ≤ 14, 14 - m, 0], P) → D'_1
  59. Vector(D, D'_1) → v
  60. Translate(e_1, v) → g_1
  61. Rotate(g_1, If[13 < m ≤ 14, ((m - 13) * π), π], D'_1) → h_1
  62. Dilate(P, If[14 < m ≤ 15, 15 - m, 0], B) → P'
  63. Vector(P, P') → w
  64. Translate(h_1, w) → k_1
  65. CircleArc(D, N, O) → p_1