Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 517-525 (2004)
Large equilateral triangles inscribed in the unit disk of a Minkowski plane
Ewa Fabinska and Marek LassakInstytut Matematyki i Fizyki ATR, Kaliskiego 7, 85-796 Bydgoszcz, Poland, e-mail: email@example.com, e-mail: firstname.lastname@example.org
Abstract: We consider a generalization of the problem of finding large equilateral triangles in the unit disks of a normed plane; we accept asymmetric unit disks, i.e. we deal with Minkowski planes. We prove that the unit disk of an arbitrary Minkowski plane permits an inscribed equilateral triangle whose oriented side lengths are at least $1.25$. We conjecture that this estimate can be improved up to $1.5$. An example shows that a better value is impossible.
Classification (MSC2000): 52A10, 52A21
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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.