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2D Symmetry & Cayley Tables

2D Symmetry & Cayley Tables. Romit Girdhar MATH 420 10/23/2012. Symmetry. What is symmetry? Symmetries of a Square 8 Motions to position a square and still be symmetric Motion : Applying a function to the square. A. B. B. C. R 90. C. D. A. D.

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2D Symmetry & Cayley Tables

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  1. 2D Symmetry & Cayley Tables Romit Girdhar MATH 420 10/23/2012

  2. Symmetry • What is symmetry? • Symmetries of a Square • 8 Motions to position a square and still be symmetric • Motion : Applying a function to the square. A B B C R90 C D A D Disclaimer: Angles will be displayed in degrees and not in radians. (Sorry!)

  3. Cayley Tables • Introduced by English mathematician, Arthur Cayley • Let’s continue with our square • D4 • Dihedral group of order 8. A B B C A D R90 H C D A D B C Diagonal Motion (D)

  4. Cayley Tables • Cayley Table for a Square (D4)

  5. Dihedral Groups • Triangle (D3) • 6 Motions • Dihedral group of order 6. • Pentagon (D5) • 10 Motions • Dihedral group of order 10. • Do you notice a pattern? • For any regular n-gon (n >= 3), the group is denoted by Dn and is called ‘Dihedral group of order 2n’.

  6. Dihedral Groups • Do we see these in our everyday life?

  7. Questions?

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