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Paula Krieg Style N-Star Construction

Paula Krieg Style N-Star Construction
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2015-12-31 23:42
TrigonometrySequenceSolid GeometryGeometric Construction
This example demonstrates how to construct a Paula Krieg style N-star pattern using GeoGebra. It involves core mathematical concepts such as symmetry, geometric construction, trigonometric functions, and sequences. Key construction steps include using commands like Circle, Point, Segment, Line, Mirror, and Sequence. Suitable for high school mathematics teaching or exploration by math enthusiasts interested in geometric symmetry and pattern design.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Segment(C, D) → a
  5. Point(c) → E
  6. Point(c) → F
  7. Segment(E, F) → b
  8. Point(c) → G
  9. Point(c) → H
  10. Segment(G, H) → d
  11. Line(A, B) → e
  12. Mirror(C, e) → C'
  13. Mirror(D, e) → D'
  14. Segment(C', D') → a'
  15. Mirror(G, e) → G'
  16. Mirror(H, e) → H'
  17. Segment(G', H') → d'
  18. Mirror(E, e) → E'
  19. Mirror(F, e) → F'
  20. Segment(E', F') → b'
  21. Sequence(Rotate[{a, a'}, ((i * 360) * ° / N), A], i, 1, N) → list1
  22. Sequence(Rotate[{b, b'}, ((i * 360) * ° / N), A], i, 1, N) → list2
  23. Sequence(Rotate[{d, d'}, ((i * 360) * ° / N), A], i, 1, N) → list3