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GoGeometry Action 147

GoGeometry Action 147
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2018-05-27 04:02
TransformationParametric EquationGeometric Construction
This is a dynamic and modifiable geometric problem example posted by Antonio Gutierrez on Twitter. It demonstrates key mathematical concepts such as line segments, conic sections, and perimeter. Using GeoGebra commands like Segment, Rotate, Angle, Ray, Point, Polygon, Line, Intersect, Min, Circle, CircleSector, Dilate, Vector, Translate, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Polygon(A, B, C) → t1, c, a_1, b
  7. Segment(A, C) → h
  8. Segment(C, B) → i
  9. Point(h) → D
  10. Line(D, f) → j
  11. Intersect(i, j) → E
  12. Line(A, E) → k
  13. Line(D, B) → l
  14. Intersect(k, l) → F
  15. Line(C, F) → m
  16. Intersect(m, f) → G
  17. Intersect(j, m) → H
  18. Min(Distance[D, A], Distance[D, C]) → e
  19. Circle(A, (0.3 * e)) → p
  20. Intersect(p, f) → I,
  21. Circle(D, 2) → q
  22. Circle(E, 2) → r
  23. Intersect(q, j, 1) → J
  24. Intersect(r, j, 2) → K
  25. Rotate(I, If[0 < d ≤ 1, (d * α), α], A) → I'
  26. CircleSector(A, I, I') → t
  27. Dilate(D, If[0 < d ≤ 1, 1 - d, 0], E) → D'
  28. Segment(D, D') → f_1
  29. Dilate(A, If[1.5 < d ≤ 2.5, 2.5 - d, 0], D) → A'
  30. Vector(A, A') → u
  31. Translate(t, u) → t'
  32. Dilate(B, If[2.5 < d ≤ 3.5, 3.5 - d, 0], D) → B'_1
  33. Segment(B, B'_1) → g_1
  34. Dilate(A, If[3.5 < d ≤ 4.5, 4.5 - d, 0], F) → A'_1
  35. Segment(A, A'_1) → h_1
  36. Dilate(F, If[4.5 < d ≤ 5.5, 5.5 - d, 0], E) → F'
  37. Segment(F, F') → i_1
  38. Dilate(C, If[6 < d ≤ 7, 7 - d, 0], H) → C'
  39. Segment(C, C') → j_1
  40. Dilate(H, If[7 < d ≤ 8, 8 - d, 0], G) → H'
  41. Segment(H, H') → k_1
  42. Dilate(D, If[9 < d ≤ 10, 10 - d, 0], H) → D'_1
  43. Segment(D, D'_1) → l_1
  44. Dilate(H, If[10 < d ≤ 11, 11 - d, 0], E) → H'_1
  45. Segment(H, H'_1) → m_1
  46. Rotate(D, If[11 < d ≤ 12, ((-(d - 11)) * π), (-π)], H) → D'_2
  47. Rotate(D'_1, If[11 < d ≤ 12, ((-(d - 11)) * π), (-π)], H) → L
  48. Segment(D'_2, L) → n_1
  49. Dilate(A, If[12 < d ≤ 13, 13 - d, 0], G) → A'_2
  50. Segment(A, A'_2) → n
  51. Rotate(A, If[13 < d ≤ 14, ((-(d - 13)) * π), (-π)], G) → A'_3
  52. Rotate(A'_2, If[13 < d ≤ 14, ((-(d - 13)) * π), (-π)], G) → M
  53. Segment(A'_3, M) → n'