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Paving the Alexanderplatz Efficiently with a Quasi-Periodic Tiling

In: Architecture and Mathematics from Antiquity to the Future

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  • Ulrich Kortenkamp

    (Martin-Luther-Universität, Institut für Mathematik)

Abstract

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.

Suggested Citation

  • Ulrich Kortenkamp, 2015. "Paving the Alexanderplatz Efficiently with a Quasi-Periodic Tiling," Springer Books, in: Kim Williams & Michael J. Ostwald (ed.), Architecture and Mathematics from Antiquity to the Future, edition 127, chapter 0, pages 473-481, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00143-2_32
    DOI: 10.1007/978-3-319-00143-2_32
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