Quasiperiodic Tilings from Ptolemy’s Theorem as Applied to Regular Polygons

Peter Stampfli and Theo P. Schaad

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 441-465 from Springer

Abstract: Abstract We apply Ptolemy’s theorem to regular polygons, obtaining integer rings. They are essential for creating substitution rules for quasiperiodic tilings using rhombic tiles. We discuss this in detail for tilings of 5-, 8-, and 12-fold rotational symmetry. Fractals are hidden in these tilings. We make them visible by using image manipulation or special substitution rules.

Keywords: Quasiperiodic tiling; Fractal; Integer ring; Geometry; Substitution method; Image manipulation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_59

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DOI: 10.1007/978-3-032-16368-4_59

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