Tilings of orthogonal polygons with similar rectangles or triangles

In this paper we prove two results about tilings of orthogonal polygons. (1) LetP be an orthogonal polygon with rational vertex coordinates and letR(u) be a rectangle with side lengthsu and 1. An orthogonal polygonP can be tiled with similar copies ofR(u) if and only ifu is algebraic and the real pa...

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Published inJournal of applied mathematics & computing Vol. 17; no. 1-2; pp. 343 - 350
Main Authors Su, Zhanjun, Ding, Ren
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.03.2005
Subjects
Algebra
Applied mathematics
Conjugates
Mathematical models
Polygons
Rectangles
Reproduction
Tiling
Triangles
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Summary:In this paper we prove two results about tilings of orthogonal polygons. (1) LetP be an orthogonal polygon with rational vertex coordinates and letR(u) be a rectangle with side lengthsu and 1. An orthogonal polygonP can be tiled with similar copies ofR(u) if and only ifu is algebraic and the real part of each of its conjugates is positive; (2) Laczkovich proved that if a triangle Δ tiles a rectangle then either Δ is a right triangle or the angles of Δ are rational multiples of π. We generalize the result of Laczkovich to orthogonal polygons.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1598-5865
1865-2085
DOI:10.1007/BF02936060