Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kanda, Shuho, Koizumi, Junnosuke
Institutions: RIKEN, The University of Tokyo
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4401202030