Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 225235 (2007) 

On Reuleaux triangles in Minkowski planesHorst Martini and Zokhrab MustafaevFaculty of Mathematics, University of Technology Chemnitz, 09107 Chemnitz, Germany, email: martini@mathematik.tuchemnitz.de; Department of Mathematics, University of HoustonClear Lake, Houston, TX 77058, USA, email: mustafaev@uhcl.eduAbstract: In this paper we prove some results on Reuleaux triangles in (Minkowski or) normed planes. For example, we reprove Wernicke's result (see \cite{We}) that the unit disc and Reuleaux triangles in a normed plane are homothets if and only if the unit circle is either an affine regular hexagon or a parallelogram. Also we show that the ratio of the area of the unit ball of a Minkowski plane to that of a Reuleaux triangle of Minkowski width 1 lies between 4 and 6. The Minkowskian analogue of Barbier's theorem is obtained, and some inequalities on areas of Reuleaux triangles are given. Keywords: Busemann area, Benson area, HolmesThompson area, Minkowski plane, constant Minkowski width, mixed volumes, Reuleaux triangles Classification (MSC2000): 52A10, 52A40, 46B20, 46B04 Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
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