The Geometry of Flex Tangents to a Cubic Curve and its Parameterizations

TL;DR

This paper explores the geometric properties of flex tangents to cubic curves, revealing how their study leads to various pseudo-parameterizations, including known and new methods.

Contribution

It introduces a geometric framework for understanding and generating pseudo-parameterizations of cubic curves through flex tangent analysis.

Findings

Revealed connections between flex tangents and pseudo-parameterizations

Identified infinitely many new pseudo-parameterizations

Unified existing parameterizations within a geometric context

Abstract

We show how the study of the geometry of the nine flex tangents to a cubic produces pseudo-parameterizations, including the ones given by Icart, Kammerer, Lercier, Renault and Farashahi, and infinitely many new ones.