Summer Institute for Mathematics at the University of
Washington 2013
|
Algebra
is nothing but written geometry; |
L'algèbre n'est
qu'une géométrie
écrite; |
Description: In this class we shall make
a transition from a very geometric notion of symmetry of two dimensional
objects and wallpaper patterns to a very algebraic notion of a group. Once we
lay down the foundations of the abstract group theory we shall go back to symmetries
and classify all possible wallpaper patterns. We shall give a (hopefully,
complete!) proof of the amazing fact that there are only 17 different wallpaper
patterns (or 17 crystallographic groups).
Our case study examples will be drawn from Escher's
extensive collection of symmetry prints. We shall devote one class to Escher's
life and work researched and presented entirely by the students.
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