We consider the classical Borsuk problem on covering a body in
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
