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The tiled circle problem

Huxley, Martin Neil 2014. The tiled circle problem. Mathematika 60 (2) , pp. 321-346. 10.1112/S0025579313000211

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How many square tiles are needed to tile a circular floor? Tiles are cut to fit the boundary. We give an algorithm for cutting, rotating and re-using the off-cut parts, so that a circular floor requires πR 2 +O(δR)+O(R 2/3 ) tiles, where R is the radius and δ is the width of the cutting tool. The algorithm applies to any oval-shaped floor whose boundary has a continuous non-zero radius of curvature. The proof of the error estimate requires methods of analytic number theory.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: University College London, School of Slavonic and East European Studies
ISSN: 0025-5793
Last Modified: 05 Mar 2019 14:25

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