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Dynamic Geometry Illustration by Tim Brzezinski (5)

Dynamic Geometry Illustration by Tim Brzezinski (5)
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2017-05-26 00:43
CirclePolygonOptimizationGeometric Construction
This example dynamically demonstrates a problem posted by Antonio Gutierrez on Twitter, involving geometric relationships between circles and rhombuses. Key math concepts include Circle, Real Numbers, Rhombus, Integral Calculus, Linear Programming/Optimization, and Frequency Distribution. The construction utilizes GeoGebra commands like Circle, Point, Intersect, CircleArc, Segment, Line, Dilate, OrthogonalLine, Distance, Angle, Rotate, Vector, and Translate, along with objects such as B, A, c, D, C, d, E, e, F, b, a, m, F'_1, n, r, K, L, f, g, h, i, C', j, G, k, H, distanceHF, distanceFE, distanceHC, α, C'_1, C''', j', C'_2, l, F', H', β, D', p. Suitable for high school and above students to explore dynamic changes and optimization in complex geometric problems.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → D
  3. Point(c) → C
  4. Circle(D, C) → d
  5. Intersect(c, d, 2) → E
  6. CircleArc(A, E, D) → e
  7. Point(e) → F
  8. Segment(E, F) → b
  9. Line(C, F) → m
  10. Dilate(F, If[5 < a ≤ 6, 6 - a, 0], E) → F'_1
  11. Segment(F, F'_1) → n
  12. Circle(C, b) → r
  13. Intersect(r, m) → K, L
  14. Segment(C, D) → f
  15. Segment(D, E) → g
  16. Segment(C, F) → h
  17. Segment(F, E) → i
  18. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], D) → C'
  19. Segment(C, C') → j
  20. Intersect(g, h) → G
  21. OrthogonalLine(D, h) → k
  22. Intersect(k, h) → H
  23. Distance(H, F) → distanceHF
  24. Distance(F, E) → distanceFE
  25. Distance(H, C) → distanceHC
  26. Angle(C, D, E) → α
  27. Rotate(C, If[1 < a ≤ 2, ((a - 1) * α), α], D) → C'_1
  28. Rotate(C', If[1 < a ≤ 2, ((a - 1) * α), α], D) → C''
  29. Segment(C'_1, C'') → j'
  30. Dilate(C, If[2 < a ≤ 3, 3 - a, 0], L) → C'_2
  31. Segment(C, C'_2) → l
  32. Dilate(F, If[3 < a ≤ 4, 4 - a, 0], E) → F'
  33. Dilate(H, If[3 < a ≤ 4, 4 - a, 0], F) → H'
  34. Angle(F, H, D) → β
  35. Dilate(D, If[6 < a ≤ 7, 7 - a, 0], H) → D'
  36. Segment(D, D') → p
  37. Line(E, l) → q
  38. Point(q) → I
  39. Angle(I, E, F) → γ
  40. Intersect(r, l, 1) → J
  41. Segment(C, C'_2) → s
  42. Dilate(L, If[3 < a ≤ 4, 4 - a, 0], H) → L'
  43. Segment(L, L') → t
  44. Rotate(F, If[7 < a ≤ 8, ((-(a - 7)) * γ), (-γ)], E) → F'_2
  45. Rotate(F'_1, If[6 < a ≤ 7, ((-(a - 6)) * γ), (-γ)], E) → M
  46. Segment(F'_2, M) → n'
  47. Dilate(E, If[8 < a ≤ 9, 9 - a, 0], C) → E'
  48. Vector(E, E') → u
  49. Translate(F'_2, u) → N
  50. Translate(M, u) → M'
  51. Segment(N, M') → n''
  52. Dilate(H, If[4 < a ≤ 5, 5 - a, 0], F) → H'_1
  53. Segment(H, H'_1) → f_1
  54. Rotate(H, If[8 < a ≤ 9, ((-(a - 8)) * π), (-π)], H) → H'_2
  55. Rotate(H'_1, If[9 < a ≤ 10, ((-(a - 9)) * π), (-π)], H) → O
  56. Segment(H'_2, O) → g_1