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Star Reflections

Star Reflections
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2019-11-19 18:26
TrigonometryTransformationGeometric Construction
This example demonstrates the geometric phenomenon of star reflections. Key mathematical concepts include reflection, trigonometric functions, and geometric transformations. Using GeoGebra commands such as Polygon, LineBisector, and Intersect, the construction of star shapes and their reflections is illustrated. 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. LineBisector(A, B) → f
  3. LineBisector(B, C) → g
  4. Intersect(f, g) → F
  5. Point(f) → G
  6. Circle(F, G) → h
  7. Intersect(h, g, 1) → H
  8. Polygon(G, H, 5) → poly2, i, j, k, l, m, I, J, K
  9. Polygon(A, G, B, H, C, I, D, J, E, K) → poly3, a_1, k_1, g_1, b_1, h_1, c_1, i_1, d_1, j_1, e_1
  10. Line(L, M) → n
  11. Line(L, N) → p
  12. Mirror(A, n) → A'
  13. Mirror(G, n) → G'
  14. Mirror(B, n) → B'
  15. Mirror(H, n) → H'
  16. Mirror(C, n) → C'
  17. Mirror(I, n) → I'
  18. Mirror(D, n) → D'
  19. Mirror(J, n) → J'
  20. Mirror(E, n) → E'
  21. Mirror(K, n) → K'
  22. Polygon(A', G', B', H', C', I', D', J', E', K') → poly3', a', k', g', b', h', c', i', d', j', e'
  23. Mirror(A', p) → A''
  24. Mirror(G', p) → G''
  25. Mirror(B', p) → B''
  26. Mirror(H', p) → H''
  27. Mirror(C', p) → C''
  28. Mirror(I', p) → I''
  29. Mirror(D', p) → D''
  30. Mirror(J', p) → J''
  31. Mirror(E', p) → E''
  32. Mirror(K', p) → K''
  33. Polygon(A'', G'', B'', H'', C'', I'', D'', J'', E'', K'') → poly3'', a'', k'', g'', b'', h'', c'', i'', d'', j'', e''