New bounds for the Heilbronn triangle problem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915984126771200 |
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| author | Agama, Theophilus |
| author_facet | Agama, Theophilus |
| contents | Using ideas from the geometry of compression, we improve on the current upper and lower bounds of the Heilbronn triangle problem. In particular, let $Δ(s)$ denote the minimal area of the triangle induced by $s$ points on a unit disk. We have the upper bound $$ Δ(s)\ll \frac{1}{s^{\frac{3}{2}-ε}} $$ for small $ε:=ε(s)>0$ and the lower bound $$ Δ(s)\gg \frac{\log s}{s\sqrt{s}}. $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_05269 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | New bounds for the Heilbronn triangle problem Agama, Theophilus Number Theory Primary 52C10, Secondary 52A38 Using ideas from the geometry of compression, we improve on the current upper and lower bounds of the Heilbronn triangle problem. In particular, let $Δ(s)$ denote the minimal area of the triangle induced by $s$ points on a unit disk. We have the upper bound $$ Δ(s)\ll \frac{1}{s^{\frac{3}{2}-ε}} $$ for small $ε:=ε(s)>0$ and the lower bound $$ Δ(s)\gg \frac{\log s}{s\sqrt{s}}. $$ |
| title | New bounds for the Heilbronn triangle problem |
| topic | Number Theory Primary 52C10, Secondary 52A38 |
| url | https://arxiv.org/abs/2006.05269 |