Paving the Alexanderplatz Efficiently with a Quasi-Periodic Tiling

Ulrich Kortenkamp

Department of Computer Science
University of Education Schwäbisch Gmünd
Oberbettringer Straße 200
73525 Schwäbisch Gmünd

Berlin's Alexanderplatz and the quasi-periodic tiling designed to pave it

In this paper we describe a mathematical approach to create an organic, yet efficient to create tiling for a large non-rectangular space, the Alexanderplatz in Berlin. We show how to use the refinement algorithm for Penrose tilings in order to create a polygonal tiling that consist of four different tiles and is quasi-periodic. We also derive, based on the refinement algorithm, bounds for the percentage of tiles of each type needed.

Another question that is addressed is whether it is possible to describe the calculated tiling in a linear form. Otherwise, it wouldn't be possible to use the tiling, as there must be a concise description suitable for the workers who lay out the concrete tiles.

About the author
Ulrich Kortenkamp is working in Mathematics, Computer Science, and Education of these disciplines. In his work in Education he is always looking for topics that exhibit the beauty of Mathematics and the usefulness of Computer Science, which is almost always true for mathematically supported architectural themes. He is also co-author of the interactive geometry software Cinderella, that constitutes a user-friendly approach to geometry with a strong mathematical foundation.
.

previous abstract

top of page

next abstract