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Explore 3-fold Symmetry in 12 Dots Pattern

Explore 3-fold Symmetry in 12 Dots Pattern
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2016-11-19 14:00
SequenceTransformationGeometric Construction
This example demonstrates the 3-fold symmetry in a 12 dots pattern. Key mathematical concepts include symmetry and rotation. Using GeoGebra commands such as Sequence, Append, Circle, Point, Polygon, and Rotate, a pattern with 3-fold symmetry can be constructed. Suitable for middle school and above students to learn about symmetry and rotation.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[(0, 1), ((k * 30))°, (0, 0)], k, 0, 11) → ring
  2. Append(ring, (0, 0)) → cir
  3. Circle((0, 0), 1) → c
  4. Point(cir) → A
  5. Point(cir) → B
  6. Point(cir) → C
  7. Point(cir) → D
  8. Point(cir) → E
  9. Polygon(A, B, C, D, E) → int, a_1, b_1, c_1, d_1, e_1
  10. Rotate(A, 120°) → A'
  11. Rotate(B, 120°) → B'
  12. Rotate(C, 120°) → C'
  13. Rotate(D, 120°) → D'
  14. Rotate(E, 120°) → E'
  15. Polygon(A', B', C', D', E') → int', a', b', c', d', e'
  16. Rotate(A, 240°) → A'_1
  17. Rotate(B, 240°) → B'_1
  18. Rotate(C, 240°) → C'_1
  19. Rotate(D, 240°) → D'_1
  20. Rotate(E, 240°) → E'_1
  21. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1) → int'_1, a'_1, b'_1, c'_1, d'_1, e'_1