On Spaces of Inscribed Triangles
Metric Geometry
2020-01-14 v2
Abstract
Meyerson's Theorem says that all but at most 2 points of any Jordan loop are vertices of inscribed equilateral triangles. We show that for any Jordan loop there are uncountable many other triangle shapes for which this same result is true. Our result comes from taking the limit of a structural result about spaces of triangles inscribed in polygons.
Cite
@article{arxiv.1908.08174,
title = {On Spaces of Inscribed Triangles},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:1908.08174},
year = {2020}
}
Comments
The proof of the result in Chapter 4 (the Component Lemma) has a gap which I cannot seem to fix. I will return the paper to the arXiv if I figure out how to fix it