On the area of ordinary hyperbolic reduced polygons

Ádám Sagmeister

On the area of ordinary hyperbolic reduced polygons

Metric Geometry 2024-09-04 v2

Authors: Ádám Sagmeister

Abstract

A convex body $R$ in the hyperbolic plane is reduced if any convex body $K\subset R$ has a smaller minimal width than $R$ . We examine the area of a family of hyperbolic reduced $n$ -gons, and prove that, within this family, regular $n$ -gons have maximal area.

Keywords

hyperbolic plane reduced polygon convex body minimal width regular n-gon maximal area

Cite

@article{arxiv.2403.11360,
  title  = {On the area of ordinary hyperbolic reduced polygons},
  author = {Ádám Sagmeister},
  journal= {arXiv preprint arXiv:2403.11360},
  year   = {2024}
}

Comments

9 pages, 1 figure

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