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Polygon Synthesizer

Polygon Synthesizer
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2016-02-03 02:23
TriangleCirclePolygonAngleTrigonometry
In collections Functions on the Domain of Space - Polygons
① This example demonstrates the dynamic construction and transformation of polygons, showing how polygons can be synthesized and decomposed. ② Core mathematical concepts include polygons, similar triangles, circles and tangents, angle relationships, trigonometric functions, and algebraic manipulation of natural numbers. ③ Construction highlights: GeoGebra commands Circle, Point, Segment, Rotate, Angle, Ray, Intersect are employed together with objects A, α, β, a, b, c, d, B, e, A′, γ, f, g, C, h₁, B′, δ, k, i, D, F, j, o, p, ε, E, C′, ζ, q, s, t, I, a₁, u, c₁, η, D′, θ₁, b₁, J. ④ Suitable for high‑school geometry and trigonometry lessons, as well as university‑level geometric modeling and exploratory activities.

GeoGebra Commands & Parameters

  1. Circle(A, a) → d
  2. Point(d) → B
  3. Segment(A, B) → e
  4. Rotate(A, α, B) → A'
  5. Angle(A, B, A') → γ
  6. Circle(B, b) → f
  7. Ray(B, A') → g
  8. Intersect(f, g) → C,
  9. Segment(B, C) → h_1
  10. Rotate(B, β, C) → B'
  11. Angle(B, C, B') → δ
  12. Circle(C, c) → k
  13. Ray(C, B') → i
  14. Intersect(k, i) → D, F
  15. Segment(C, D) → j
  16. Circle(D, o) → p
  17. Intersect(p, j) → E,
  18. Rotate(C, ε, D) → C'
  19. Angle(C, D, C') → ζ
  20. Ray(D, C') → q
  21. Circle(D, o) → s
  22. Ray(D, C') → t
  23. Intersect(s, t) → I,
  24. Segment(D, I) → a_1
  25. Circle(I, u) → c_1
  26. Rotate(D, η, I) → D'
  27. Angle(D, I, D') → θ_1
  28. Ray(I, D') → b_1
  29. Intersect(c_1, b_1) → J,
  30. Segment(I, J) → d_1
  31. Ray(C, A) → m
  32. Ray(D, A) → l
  33. Ray(I, A) → n
  34. Angle(I, A, B) → κ
  35. Angle(D, A, B) → θ
  36. Angle(C, A, B) → λ