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**2D Symmetry & Cayley Tables**

Romit Girdhar MATH 420 10/23/2012

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**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!)

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**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)

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Cayley Tables Cayley Table for a Square (D4)

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**Dihedral Groups Triangle (D3) Pentagon (D5) Do you notice a pattern?**

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’.

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Dihedral Groups Do we see these in our everyday life?

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Questions?

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Confidential 1. 2 Lets review what we have learned Polygons: A polygon is a closed plane figure made up of 3 or more line segments. Types of Polygons:

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