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Polygon Exploration

Polygon Exploration
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2016-01-19 06:05
PolygonTrigonometryTransformation
In collections Functions on the Domain of Space - Polygons
This example demonstrates the exploration of polygons, involving trigonometric functions and geometric transformations. Using GeoGebra commands such as Polygon, Angle, and Segment, the shape and position of the polygon can be dynamically changed. Suitable for high school mathematics education, particularly in geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly2, c_1, a_1, b_1
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Angle(A, B, C) → β3
  4. Angle(B, C, A) → γ3
  5. Angle(C, A, B) → α3
  6. Angle(B, C, D) → γ4
  7. Angle(C, D, A) → δ
  8. Angle(D, A, B) → α4
  9. Angle(A, B, C) → β4
  10. Segment(E, I) → g
  11. Segment(F, J) → h
  12. Segment(G, K) → i
  13. Segment(H, L) → j
  14. Segment(E, M) → k
  15. Segment(P, T) → n
  16. Segment(R, V) → p
  17. Segment(Q, U) → q
  18. Segment(S, W) → r
  19. Segment(A_1, D_1) → s
  20. Segment(Z, C_1) → t
  21. Segment(B_1, E_1) → d_1
  22. Segment(F, N) → m
  23. Segment(G, O) → l
  24. Polygon(A, B, C, D, F_1) → poly3, a_2, b_2, c_2, d_2, f_1
  25. Angle(B, C, D) → α
  26. Angle(C, D, F_1) → β
  27. Angle(D, F_1, A) → γ
  28. Angle(F_1, A, B) → ε
  29. Segment((x(E), 0), (x(E), a_2 / p5)) → e_1
  30. Segment((x(F), 0), (x(F), b_2 / p5)) → g_1
  31. Segment((x(G), 0), (x(G), c_2 / p5)) → h_1
  32. Segment((x(H), 0), (x(H), d_2 / p5)) → i_1
  33. Segment((x(H5), 0), (x(H5), f_1 / p5)) → j_1
  34. Segment((x(P), 0), (x(P), ε / ((3 * π)))) → k_1
  35. Segment((x(Q), 0), (x(Q), β3 / ((3 * π)))) → l_1
  36. Segment((x(R), 0), (x(R), α / ((3 * π)))) → m_1
  37. Segment((x(S), 0), (x(S), β / ((3 * π)))) → n_1
  38. Segment((x(S5), 0), (x(S5), γ / ((3 * π)))) → p_1