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Tilings of orthogonal polygons with similar rectangles or triangles

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Hebei Normal University, 050016, Shijiazhuang, P. R. China

    Zhanjun Su & Ren Ding

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  1. Zhanjun Su
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  2. Ren Ding
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Correspondence to Zhanjun Su.

Additional information

This research was supported by NSFH and SFHEM

Zhanjun Su received his BSc and MSc from the Hebei Normal University. Since 2001 he has been a graduate student for Ph. D. degree at Hebei Normal University under the direction of Prof. Ren Ding. His research interests focus on discrete geometry, convex geometry and combinatorial geometry.

Ren Ding is a professor of mathematics, supervising Ph. D. programs at Hebei Normal University. His research interests focus on discrete geometry, convex geometry and combinatorial geometry.

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Su, Z., Ding, R. Tilings of orthogonal polygons with similar rectangles or triangles. JAMC 17, 343–350 (2005). https://doi.org/10.1007/BF02936060

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  • DOI: https://doi.org/10.1007/BF02936060

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