Triangles of nearly equal area
Swanepoel, K.
(2021).
Triangles of nearly equal area.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry,
62(1), 219 - 227.
https://doi.org/10.1007/s13366-021-00567-2
(2021).
Triangles of nearly equal area.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry,
62(1), 219 - 227.
https://doi.org/10.1007/s13366-021-00567-2
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.
