Another Proof of Segre's Theorem about Ovals
Number Theory
2026-05-19 v2 Combinatorics
Abstract
In 1955 B. Segre showed that any oval in a projective plane over a finite field of odd order is a conic. His proof constructs a conic which matches the oval in some points and tangents, and then shows that it actually coincides with the oval. The different proof given here parametrizes an affine piece of the oval and shows directly that the parametrization is given by a polynomial of degree .
Cite
@article{arxiv.1311.3082,
title = {Another Proof of Segre's Theorem about Ovals},
author = {Peter Müller},
journal= {arXiv preprint arXiv:1311.3082},
year = {2026}
}
Comments
4 pages, enhanced introduction and simplified proof