A lower bound for Heilbronn's triangle-problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866917074172903424 |
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| author | Ellmann, Gabor |
| author_facet | Ellmann, Gabor |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_03297 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A lower bound for Heilbronn's triangle-problem Ellmann, Gabor Metric Geometry Number Theory 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). |
| title | A lower bound for Heilbronn's triangle-problem |
| topic | Metric Geometry Number Theory |
| url | https://arxiv.org/abs/1703.03297 |