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THE TILED CIRCLE PROBLEM
Author(s) -
Huxley M. N.
Publication year - 2014
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579313000211
Subject(s) - mathematics , tile , boundary (topology) , radius , radius of curvature , curvature , geometry , square (algebra) , circle packing , mathematical analysis , zero (linguistics) , mean curvature , mean curvature flow , computer science , art , linguistics , philosophy , computer security , visual arts
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 π R 2 + O ( δ R ) + 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.