A disc packing in the plane is compact if its contact graph a triangulation. There are nine values of r such that by discs radii 1 and exists. For each these values, we prove maximal density over all packings reached for packing. We describe give density.

It is well-known that during tillage operations suprising items may appear below the soil surface in agricultural lands. Sometimes a stone/rock or solid root can cause major damage to equipments. These rocks and roots impacts on equipment. In order eliminate minimize impact of these forces, shock absorbing equipment used provides connection between disc harrow chassis. The most commonly materia...

A compact (orientable or non-orientable) surface of genus g is said to be extremal if it contains an extremal disc, that is, a disc of the largest radius determined only by g. The present paper concerns non-orientable extremal surfaces of genus 5. We represent the surfaces as side-pairing patterns of a hyperbolic regular 24-gon, that is, a generic fundamental region of an NEC group uniformizing...