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DECOMPOSITION OF BALLS INTO CONGRUENT PIECES

Part of: General convexity Metric geometry

Published online by Cambridge University Press:  21 January 2011

Gergely Kiss  and
Miklós Laczkovich
Gergely Kiss
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C 1117, Hungary (email: kisss@cs.elte.hu)
Miklós Laczkovich
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C 1117, Hungary Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, U.K. (email: laczk@cs.elte.hu)
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Abstract

We prove that if 3|d, then the d-dimensional balls are m-divisible for every m large enough. In particular, the three-dimensional balls are m-divisible for every m≥22.

MSC classification

Secondary: 52A15: Convex sets in $3$ dimensions (including convex surfaces) 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 51F20: Congruence and orthogonality

Information

Type
Research Article
Information
Mathematika , Volume 57 , Issue 1 , January 2011 , pp. 89 - 107
Copyright
Copyright © University College London 2011

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