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Gyration Points in Frieze Symmetry Demo

Gyration Points in Frieze Symmetry Demo
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2020-01-31 22:59
CirclePolygonTrigonometryTransformationGeometric Construction
This example demonstrates how to identify and construct gyration points in frieze patterns, involving rotation and symmetry. Key math concepts include rotation, symmetry, similar triangles, parallelograms, and geometric transformations. GeoGebra commands like Circle, Rotate, Polygon, and Midpoint are used in the construction. Suitable for high school students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, α, A) → B'
  3. Rotate(B, (-α), A) → B'_1
  4. Polygon(A, B', B, B'_1) → q1, a, b', b, b'_1
  5. Midpoint(a) → C
  6. Midpoint(b) → D
  7. Midpoint(A, C) → E
  8. Midpoint(C, B') → F
  9. Midpoint(B'_1, D) → G
  10. Midpoint(D, B) → H
  11. Polygon(E, B'_1, G, H) → q2, e, f, g, h
  12. Rotate(A, 180°, I) → A'
  13. Rotate(B', 180°, I) → B''
  14. Rotate(B, 180°, I) → B'_2
  15. Rotate(B'_1, 180°, I) → J
  16. Polygon(A', B'', B'_2, J) → q1', a', b'', b'_2, j
  17. Rotate(E, 180°, I) → E'
  18. Rotate(B'_1, 180°, I) → K
  19. Rotate(G, 180°, I) → G'
  20. Rotate(H, 180°, I) → H'
  21. Polygon(E', K, G', H') → q2', e', k, g', h'