 |
Universität Augsburg
|
|
|
Universität Augsburg
|
|
Professor Dr. Jost-Hinrich Eschenburg
Universität Augsburg
spricht am
Montag, 25. Januar 2016
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| As finite beings with a finite set of ideas, how can we invent a tiling of the whole infinite plane (complete tiling)? In art, two answers have been developed: Periodicity (a finite domain repeats itself in two directions) and Self Similarity (a small area determines the pattern for a larger area). In 1974, Roger Penrose introduced a class of tilings which are not periodic but have a certain self similarity property. They are constructed from two types of tiles, based on the geometry of the regular pentagon. So far there is no valid constuctive definition for Penrose tilings which are extendible to complete ones. Matching rules (see Wikipedia article on Penrose tilings) are not sufficient as we will see. One way to construct complete tilings is by projecting a strip of a regular grid in higher dimensions. However, we will give an example of a Penrose tiling which does not arise in this way. We use an extremely narrow definition of Penrose tilings which seems to completely determine those patterns, but still it allows uncountably many different patterns, including all projection tilings. This finding was heavily influenced by some 400 years old Islamic patterns at Isfahan, Iran. (Common work with H.J. Rivertz, Trondheim, Norway) |
| Hierzu ergeht herzliche Einladung. |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).