Triangles of nearly equal area

被引：0
|
作者：
Swanepoel, Konrad J. [1 ]
机构：
[1] London Sch Econ, London, England
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2021年 / 62卷 / 01期
关键词：
Sidon set; Triangle area; Golden ratio; Plastic number; Morphic number;
D O I：
10.1007/s13366-021-00567-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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/n(2)). Ifwe 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.
引用
收藏
页码：219 / 227
页数：9
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