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Triangles of nearly equal area

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2021) Triangles of nearly equal area. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 62 (1). 219 - 227. ISSN 0138-4821

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Identification Number: 10.1007/s13366-021-00567-2

Abstract

Given any n points in the plane, not all on the same line, there exist two non-collinear triples such that the ratio of the areas of the triangles they determine, differs from 1 by at most O(log n/n2). If we furthermore insist that the two triangles have a common edge, then there are two with area ratios differing from 1 by at most O(1/n). This improves some results of Ophir and Pinchasi (Discrete Appl. Math. 174 (2014), 122–127). We also give some constructions for these and related problems.

Item Type: Article
Official URL: https://www.springer.com/journal/13366
Additional Information: © 2021 The Author
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Feb 2021 11:18
Last Modified: 20 Sep 2021 03:20
URI: http://eprints.lse.ac.uk/id/eprint/108667

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