Mathematisches Institut der Universität München - B. Pareigis ## Prof. Dr. Bodo Pareigis## Proseminar: Crystallographic groups (Kristallographische Gruppen) (SS 2001)-
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- Time: Wednesday, 11:15 am
- Room: 251
- Planning session: Tuesday, February 6, 2001, 1:15 pm, Room 251
- Contents: The goal of the undergraduate seminar is to classify
the plane crystallographic groups, i.e., the symmetry groups of
ornaments in the plane. Although there are plenty of ornaments of
different colours and shapes, it turns out that, for the symmetries
underlying these ornaments, there are only 17 distinct types. It seems
that this fact was already known to the arabic craftsmen during the
middle ages, since in their buildings of that time all these types can
be found. The rigourous mathematical treatment of this classification,
however, was first carried out at the end of the nineteenth century. In
our times, these symmetries have attracted greater attention through
the work of M. C. Escher.
The undergraduate seminar is directed at students of mathematics before the Vordiplom from their second semester on upwards. It provides a good opportunity the apply the notions learned in linear algebra to an attractive problem and thereby to enhance their understanding. In the planning of the talks, care has been taken to partially repeat the tools needed from linear algebra, so that the seminar is also helpful to rework the linear algebra course. - Seminar program (german, dvi)
- Seminar text
- List of 17 plane crystallographischen groups (by NN)
- Escher Web Sketch
- Selected works of M. C. Escher
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