ﻻ يوجد ملخص باللغة العربية
We give a simple proof of T. Stehlings result, that in any normal tiling of the plane with convex polygons with number of sides not less than six, all tiles except the finite number are hexagons.
Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation numbers for such maps. In constrast to the classic
We prove that for every $N e 4$ there is only one right triangle that tiles the regular $N$-gon.
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be difficult. To approach it, we define and count families of subs
We give an improvement of the Caratheodory theorem for strong convexity (ball convexity) in $mathbb R^n$, reducing the Caratheodory number to $n$ in several cases; and show that the Caratheodory number cannot be smaller than $n$ for an arbitrary gaug
In this note, we give a short solution of the kissing number problem in dimension three.