We find a large number of" geometric separator theorems" such as: I: Given N disjoint
isooriented squares in the plane, there exists a rectangle with/spl les/2N/3 squares …

Geometry is a classical core part of mathematics which, with its birth, marked the beginning
of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in …

This is a review of various problems and results on the illumination of convex bodies in the
spirit of combinatorial geometry. The topics under review are: history of the Gohberg-Markus …

At a first glance, the problem of illuminating the boundary of a convex body by external light
sources and the problem of covering a convex body by its smaller positive homothetic …

An Estimate for the Problem of Illumination of the Boundary of a Convex Body in E3 Page 1
Geometriae Dedicata 75: 275–285, 1999. © 1999 Kluwer Academic Publishers. Printed in the …

The main result of this paper is the following theorem. If P is a convex polytope of Ed with
affine symmetry, then P can be illuminated by eight (d-3)-dimensional affine subspaces (two …

Let Sn be an n-dimensional simplex and Γp (Sn) be the smallest positive number γ such that
Sn can be covered by p translates of γSn. We obtain an upper bound of the least positive …

We show that every three-dimensional convex body can be covered by 14 smaller
homothetic copies. The previous result was 16 established by Papadoperakis in 1999, while …

Let H_n H n be the minimal number of smaller homothetic copies of an n-dimensional
convex body required to cover the whole body. Equivalently, H_n H n can be defined via …

Summary The Illumination Conjecture was raised independently by Boltyanski and
Hadwiger in 1960. According to this conjecture any<! CDATA<! CDATA<! CDATA >>>d …