Work

A lower bound for Heilbronn's triangle-problem

Year: 2017

Type: preprint

Abstract: Let n points be placed on a closed convex domain on the plane, no three points on a straight line. A conjecture by H. A. Heilbronn (before 1950) stated that on the convex domain of unit area the smallest triangle defined by these points has an area not larger than O(n^-2). Here is shown a construction of a set of n points on a unit circle where any of the triangles have an area not less than O(n^-3/2 * (log n)^-7/2).

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1703.03297

Author: Ellmann, Gabor

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4293227739

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