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Borsuk's problem, Boltyanski's illumination problem, and circumradius

Arthur Bikeev

Vol. 12 (2023), No. 3, 223–240
Abstract

We consider the classical Borsuk problem on covering a body in n by parts of smaller diameter, and related problems. The aim of this paper is to prove some estimates depending on circumradius of a body.

Keywords
Borsuk's problem, Boltyanski's illumination problem, illumination, illumination number, circumcenter, circumradius, constant width, covering of a body by its positive homothetic copies, combinatorial geometry
Mathematical Subject Classification
Primary: 51-XX, 52-XX
Milestones
Received: 23 March 2023
Revised: 7 May 2023
Accepted: 22 May 2023
Published: 23 September 2023
Authors
Arthur Bikeev
Moscow Institute of Physics and Technology
Dolgoprudny
Russia