Department Mathematik



Yorck Sommerhäuser


Cristallographic groups
(Kristallographische Gruppen)

  • Summer semester 2001
  • 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 cristallographic 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)
  • List of the 17 plane cristallographic groups (by Michael Helbig)
  • Escher Web Sketch
  • Selected works of M. C. Escher