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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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:	11 Sep 2025 10:32
URI:	http://eprints.lse.ac.uk/id/eprint/108667

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