The mathematics behind Escher's prints: a round trip journey from symmetry to groups and back
The mathematics behind Escher's prints: a round trip journey from symmetry to groups and back |
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Summer Institute for Mathematics at the University of Washington 2009
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| Algebra is nothing but written geometry; | L'algèbre n'est qu'une géométrie écrite; |
| Geometry is nothing but pictured algebra. | la géométrie n'est qu'une algèbre figurée. |
| Sophie Germain |
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 Eshcher's life and work researched and presented entirely by the students.
More information about the course can be found here: Course webpage.
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