On iterated circumcenter sequences
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911971016704000 |
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| author | Kanda, Shuho Koizumi, Junnosuke |
| author_facet | Kanda, Shuho Koizumi, Junnosuke |
| contents | An iterated circumcenter sequence (ICS) in dimension $d$ is a sequence of points in $\mathbb{R}^d$ where each point is the circumcenter of the preceding $d+1$ points. The purpose of this paper is to completely determine the parameter space of ICSs and its subspace consisting of periodic ICSs. In particular, we prove Goddyn's conjecture on periodic ICSs, which was independently proven recently by Ardanuy. We also prove the existence of a periodic ICS in any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On iterated circumcenter sequences Kanda, Shuho Koizumi, Junnosuke Combinatorics Metric Geometry 51M04, 52C35 An iterated circumcenter sequence (ICS) in dimension $d$ is a sequence of points in $\mathbb{R}^d$ where each point is the circumcenter of the preceding $d+1$ points. The purpose of this paper is to completely determine the parameter space of ICSs and its subspace consisting of periodic ICSs. In particular, we prove Goddyn's conjecture on periodic ICSs, which was independently proven recently by Ardanuy. We also prove the existence of a periodic ICS in any dimension. |
| title | On iterated circumcenter sequences |
| topic | Combinatorics Metric Geometry 51M04, 52C35 |
| url | https://arxiv.org/abs/2407.19767 |