Tilings of polygons composed of equal rectangles by similar rectangles
Ivan Novikov
TL;DR
This paper characterizes all quadratic irrational ratios for which polygons made of equal rectangles can be tiled by similar rectangles with the same ratio, providing a complete classification of such tilings.
Contribution
It identifies all quadratic irrational ratios allowing tilings of polygons composed of equal rectangles by similar rectangles with the same ratio.
Findings
Complete classification of quadratic irrational ratios for tilings
Identification of conditions for tiling polygons with similar rectangles
Mathematical characterization of tiling possibilities
Abstract
Let a polygon be composed of equal rectangles. We find all quadratic irrationals r for which the polygon can be tiled by similar rectangles with given side ratio r.
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Taxonomy
TopicsMathematics and Applications · Quasicrystal Structures and Properties · graph theory and CDMA systems