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Rotational Symmetry (Cn group)

Rotational Symmetry (Cn group)
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2014-10-09 09:37
CircleTransformationGeometric Construction
In collections Symmetry Explorations
This applet explores Cn symmetrical patterns (up to n=20). It involves the concept of rotational symmetry. Using the Rotate command, it constructs patterns with rotational symmetry. Suitable for high school geometry lessons to help students understand rotational symmetry and its applications.

GeoGebra Commands & Parameters

  1. Rotate(B, α, A) → B'
  2. Rotate(B', α, A) → B''
  3. Rotate(B'', α, A) → B'''
  4. Rotate(B''', α, A) → C
  5. Rotate(C, α, A) → C'
  6. Rotate(C', α, A) → C''
  7. Rotate(C'', α, A) → C'''
  8. Rotate(C''', α, A) → D
  9. Rotate(D, α, A) → D'
  10. Rotate(D', α, A) → D''
  11. Rotate(D'', α, A) → D'''
  12. Rotate(D''', α, A) → E
  13. Rotate(E, α, A) → E'
  14. Rotate(E', α, A) → E''
  15. Rotate(E'', α, A) → E'''
  16. Rotate(E''', α, A) → F
  17. Rotate(F, α, A) → F'
  18. Rotate(F', α, A) → F''
  19. Rotate(F'', α, A) → F'''

AI Drawing Prompt Reference

Create a rotational symmetry pattern with point A as the rotation center. Start from point B and rotate to generate B', B'', B''', then from C to generate C', C'', C''', and so on until F', F'', F'''. This will form a hexagonal pattern demonstrating rotational symmetry C6.
The prompt above was compiled from the original drawing commands and is for reference only.