Packing, covering and tiling is a fascinating subject in pure mathematics. It mainly deals with
arrangement patterns and efficiencies of geometric objects. This subject has a long and rich …

What configuration of N point charges on a conducting sphere minimizes the Coulombic
energy? JJ Thomson posed this question in 1904. For N≤ 112, numerical methods have …

Herein I address the current number of plates, the number there should be, and whether
there is a pattern in the plate mosaic. Related issues are the optimal sizes and shapes of …

Digital media manipulation has become easily performed at personal level with the rapidly
growth of Technology. Presenting an issue of protecting digital media integrity …

How must n equal circles (spherical caps) of given angular radius r be arranged on the
surface of a sphere so that the area covered by the circles will be as large as possible? In …

In this paper a brief account is devoted to structural forms related to geodesic domes
appearance in nature. It is shown how geodesic domes helped researchers outside …

The one-round discrete Voronoi game, with respect to an n-point user set U, consists of two
players Player 1 (P 1) and Player 2 (P 2). At first, P 1 chooses a set of facilities F 1 following …

Federated learning in satellites offers several advantages. Firstly, it ensures data privacy
and security, as sensitive data remains on the satellites and is not transmitted to a central …

Amongst the convex polyhedra with n faces circumscribed about the unit sphere, which has
the minimum surface area? This is the isoperimetric problem in discrete geometry which is …

An overview of the authors' work (partly in collaboration with WD Smith) on the problems of
packing equal nonoverlapping spherical caps on a sphere in d dimensions, covering the …