Number Theory

    

An Improved Lower Bound of Heilbronn's Triangle Problem

Authors: Theophilus Agama

Using the method of compression we improve on the current lower bound of Heilbronn's triangle problem. In particular, by letting $Delta(s)$ denotes the minimal area of the triangle induced by $s$ points in a unit disc. Then we have the lower boundbegin{align}Delta(s)gg frac{log s}{ssqrt{s}}.onumberend{align}

Comments: 10 Pages. This paper has been technically and substantially improved.

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Submission history

[v1] 2020-06-05 18:36:03
[v2] 2020-06-12 12:01:57
[v3] 2021-08-17 18:40:29
[v4] 2022-01-23 13:28:07
[v5] 2024-03-19 05:54:19

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