关于迭代圆心序列

arXiv - MATH - Metric Geometry Pub Date : 2024-07-29 DOI:arxiv-2407.19767

Shuho Kanda, Junnosuke Koizumi

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引用次数: 0

摘要

维数$d$的迭代圆周中心序列（ICS）是$\mathbb{R}^d$中的一个点序列，其中每个点都是前d+1$个点的圆周中心。本文的目的是完全确定 ICS 的参数空间及其由周期 ICS 组成的子空间。特别是，我们证明了戈登关于周期性 ICS 的猜想，该猜想最近由阿达努伊独立证明。我们还证明了任何维度上非周期性 ICS 的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On iterated circumcenter sequences

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.

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arXiv - MATH - Metric Geometry

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