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Geometric Transformations and Polygons by Arthur Lee

Geometric Transformations and Polygons by Arthur Lee
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2016-02-08 11:14
PolygonTrigonometry
This example demonstrates the process of generating polygons through geometric transformations such as mirroring and rotating. Key mathematical concepts include polygons, trigonometric functions, and transformations. Using GeoGebra commands like Polygon, Mirror, and Rotate, dynamic observations of how geometric transformations affect polygons can be made. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, a, b, c, d, e, C, D, E
  2. Mirror(B, A) → B'
  3. Rotate(B', 72°, B) → B''
  4. Rotate(B, 108°, B'') → B'_1
  5. Polygon(B, B'', B'_1, B') → poly2, b_1, b'', b'_1, b'
  6. Circle(D, A, B) → f
  7. Center(f) → F
  8. Rotate(B, 72°, F) → B'_2
  9. Rotate(B'', 72°, F) → B'''
  10. Rotate(B'_1, 72°, F) → G
  11. Rotate(B', 72°, F) → B''_1
  12. Polygon(B'_2, B''', G, B''_1) → poly2', b'_2, b''', g, b''_1
  13. Rotate(B'_2, 72°, F) → H
  14. Rotate(B''', 72°, F) → I
  15. Rotate(G, 72°, F) → G'
  16. Rotate(B''_1, 72°, F) → J
  17. Polygon(H, I, G', J) → poly2'', h, i, g', j
  18. Rotate(H, 72°, F) → H'
  19. Rotate(I, 72°, F) → I'
  20. Rotate(G', 72°, F) → G''
  21. Rotate(J, 72°, F) → J'
  22. Polygon(H', I', G'', J') → poly2''', h', i', g'', j'
  23. Rotate(H', 72°, F) → H''
  24. Rotate(I', 72°, F) → I''
  25. Rotate(G'', 72°, F) → G'''
  26. Rotate(J', 72°, F) → J''
  27. Polygon(H'', I'', G''', J'') → poly3, h'', i'', g''', j''
  28. Ray(D, E) → k
  29. Ray(B'_1, B') → l
  30. Intersect(k, l) → K
  31. Polygon(A, B', K, E) → poly4, a_1, b'_3, k_1, e_1
  32. Midpoint(J'', I'') → L
  33. Mirror(A, L) → A'
  34. Mirror(B', L) → B''_2
  35. Mirror(K, L) → K'
  36. Mirror(E, L) → E'
  37. Polygon(A', B''_2, K', E') → poly4', a', b''_2, k', e'
  38. Sequence(Polygon[Rotate[A, ((k * 72))°, F], Rotate[B', ((k * 72))°, F], Rotate[K, ((k * 72))°, F], Rotate[E, ((k * 72))°, F]], k, 1, 5) → list1
  39. Sequence(Polygon[Rotate[A', ((k * 72))°, F], Rotate[B''_2, ((k * 72))°, F], Rotate[K', ((k * 72))°, F], Rotate[E', ((k * 72))°, F]], k, 1, 5) → list2