arXiv subjects

Fyodor Sharov

Publications and source records attributed to Fyodor Sharov.

2 recordsLinked to original sources

arXiv2017

x-area

We give a new simple proof of Dehn's theorem by generalizing the notion of area. The method proposed in the present article is actually the "translation" of the method of additive functions into the elementary math language.

math.CO↗

arXiv2016

Dissection of a rectangle into rectangles with given side ratios

Given a collection of N rectangles such that the side ratio of each one is a quadratic irrationality, we find all rectangles which can be tiled by rectangles similar to one of the given ones. It means that each possible shape can be used several times or not used at all, so that the number of rectangles in the tiling is not necessarily equal to N.

math.CO↗