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Romit Girdhar MATH 420 10/23/2012. What is symmetry? Symmetries of a Square 8 Motions to position a square and still be symmetric Motion : Applying a.

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Presentation on theme: "Romit Girdhar MATH 420 10/23/2012. What is symmetry? Symmetries of a Square 8 Motions to position a square and still be symmetric Motion : Applying a."— Presentation transcript:

1 Romit Girdhar MATH 420 10/23/2012

2 What is symmetry? Symmetries of a Square 8 Motions to position a square and still be symmetric Motion : Applying a function to the square. R 90 AB CD BC AD Disclaimer: Angles will be displayed in degrees and not in radians. (Sorry!)

3 Introduced by English mathematician, Arthur Cayley Lets continue with our square D 4 Dihedral group of order 8. R 90 AB CD BC AD H AD BC Diagonal Motion (D)

4 Cayley Table for a Square (D 4 )

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

6 Do we see these in our everyday life?

7


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