Perimeter approximation of convex discs in the hyperbolic plane and on the sphere
Metric Geometry
2026-04-13 v1
Abstract
Eggleston (1957) proved that in the Euclidean plane the best approximating convex -gon to a convex disc is always inscribed in if we measure the distance by perimeter deviation. We prove that the analogue of Eggleston's statement holds in the hyperbolic plane, and we give an example showing that it fails on the sphere.
Cite
@article{arxiv.1902.03655,
title = {Perimeter approximation of convex discs in the hyperbolic plane and on the sphere},
author = {Ferenc Fodor},
journal= {arXiv preprint arXiv:1902.03655},
year = {2026}
}