Conics in normed planes

TL;DR

This paper explores how classical conic definitions extend to normed planes, revealing that different definitions generally produce distinct classes of curves in this broader setting.

Contribution

It systematically analyzes the extension of Euclidean conic definitions to normed planes and demonstrates their differences in this generalized context.

Findings

Different conic definitions yield distinct classes of curves in normed planes

Most classical conic definitions do not coincide in the normed setting

The study highlights the complexity of generalizing Euclidean conics

Abstract

We study the generalized analogues of conics for normed planes by using the following natural approach: It is well known that there are different metrical definitions of conics in the Euclidean plane. We investigate how these definitions extend to normed planes, and we show that in this more general framework these different definitions yield, in almost all cases, different classes of curves.