I. V. Novikov, “Cutting Polygons Composed of Equal Rectangles into Similar Rectangles”, Mat. Zametki, 2021, Volume 110, Issue 5,Pages <nobr>736

Cutting Polygons Composed of Equal Rectangles into Similar Rectangles

I. V. Novikov

National Research University "Higher School of Economics", Moscow

Abstract: Assume that a polygon is composed of equal rectangles. We find all quadratic irrationalities $r$ for which the polygon under study can be cut into similar rectangles with aspect ratio $r$.

Keywords: cutting, tiling, additive function, rectangle, quadratic irrationality.

UDC: 519.1

Received: 12.03.2019

DOI: 10.4213/mzm13262