Discrete Conics

TL;DR

This paper introduces discrete conics, polygonal analogues of classical conics, exploring their properties and natural constructions, including discrete negative pedal and group actions on focus-sharing conics.

Contribution

It defines discrete conics and demonstrates their properties and natural geometric constructions, bridging discrete geometry with classical conic theory.

Findings

Discrete conics satisfy properties similar to classical conics.

They arise from discrete negative pedal constructions.

Group actions on focus-sharing pencils generate discrete conics.

Abstract

In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the discrete negative pedal construction and an action of a group acting on a focus-sharing pencil of conics.