An affine characterization of quadratic curves

TL;DR

This paper provides an affine geometric characterization of quadratic curves by examining their curvature properties through the affine Taylor expansion, linking polynomial features to curve classification.

Contribution

It introduces a novel affine characterization of quadratic curves using curvature analysis derived from the affine Taylor expansion.

Findings

Characterization of quadratic curves via curvature properties

Connection between polynomial coefficients and curve classification

Method based on affine Taylor expansion analysis

Abstract

By analyzing the affine Taylor expansion of a non-degenerate plane curve, we obtain characterizations of classes of such curves via curvature properties of the gravity curve. The proof is based on an analysis of the degree parity and leading coefficients of polynomials occurring in the expansion.