Discrete & Computational Geometry

, Volume 48, Issue 3, pp 766–776 | Cite as

Kadets-Type Theorems for Partitions of a Convex Body



For convex partitions of a convex body B, we try to put a homothetic copy of B into each set of the partition so that the sum of the homothety coefficients is at least 1. In the plane this can be done for an arbitrary partition, while in higher dimensions we need certain restrictions on the partition.


The Tarski plank problem The Kadets theorem 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems RASMoscowRussia
  2. 2.Dept. of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Laboratory of Discrete and Computational GeometryYaroslavl State UniversityYaroslavlRussia

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