Constructive curves in non-Euclidean planes

TL;DR

This paper reviews the development and current state of conics and roulettes in four non-Euclidean planes, highlighting historical and recent literature to compare their properties across different geometries.

Contribution

It provides a comprehensive overview of classical and recent results on conics and roulettes in four non-Euclidean geometries, including literature from the eighteenth century to present.

Findings

Comparison of conics and roulettes across four non-Euclidean planes.

Historical and recent literature on non-Euclidean conics compiled.

Subjective analysis of differences between geometries.

Abstract

In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The comparison of the four non-Euclidean planes, in terms of the known results on conics and roulettes, reflects only the very subjective view of the author.