Equisectional equivalence of triangles
Metric Geometry
2016-08-30 v1
Abstract
We study equivalence relation of the set of triangles generated by similarity and operation on a triangle to get a new one by joining division points of three edges with the same ratio. Using the moduli space of similarity classes of triangles introduced by Nakamura and Oguiso, we give characterization of equivalent triangles in terms of circles of Apollonius (or hyperbolic pencil of circles) and properties of special equivalent triangles. We also study rationality problem and constructibility problem.
Keywords
Cite
@article{arxiv.1608.08087,
title = {Equisectional equivalence of triangles},
author = {Jun O'Hara},
journal= {arXiv preprint arXiv:1608.08087},
year = {2016}
}
Comments
10 pages, 6 figures