Undergraduate Mathematics/The Group Theory of the Symmetries of Simple Shapes

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Undergraduate Mathematics

Undergraduate Mathematics/The Group Theory of the Symmetries of Simple Shapes 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  1. Undergraduate Mathematics/Cyclic group 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  2. Undergraduate Mathematics/Dyhedral group 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  3. Undergraduate Mathematics/Cosets and Quotient Groups 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  4. Undergraduate Mathematics/Sylow theorems 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  5. Undergraduate Mathematics/Abelian group 0% developed  as of Mar 17, 2014 (Mar 17, 2014)
  6. Undergraduate Mathematics/Burnside's lemma 0% developed  as of Mar 17, 2014 (Mar 17, 2014)

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In this module, we consider the symmetries of 2D sets of points such as those pictured below.

We ask questions like:

  1. Why does the combination of symmetries form a group?
  2. Which combinations of symmetries are the same?
  3. How many distinct symmetries are there for a given set?
  4. Which sets have the same symmetry groups?