Cinderella, quadrilaterals and conics

TL;DR

This paper explores properties of quadrilaterals inscribed in and circumscribed about conics, extending classical projective geometry results and demonstrating how software like Cinderella can inspire new mathematical insights.

Contribution

It provides new proofs of Poncelet's theorem for quadrilaterals and introduces modern software tools to enhance research in pure and applied geometry.

Findings

Extended known results in projective geometry of conics.

Proved Poncelet's theorem for quadrilaterals using elementary methods.

Showcased how software Cinderella aids in mathematical discovery.

Abstract

We study quadrilaterals inscribed and circumscribed about conics. Our research is guided by experiments in software Cinderella. We extend the known results in projective geometry of conics and show how modern mathematical software brings new ideas in pure and applied mathematics. Poncelet theorem for quadrilaterals is proved by elementary means together with Poncelet's grid property.