Interesting Esoterica

Another Proof of Segre's Theorem about Ovals

Article by Müller, Peter
  • Published in 2013
  • Added on
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 then shows that it actually coincides with the oval. Here we give another proof. We describe the oval by a possibly high degree polynomial, and then show that the degree is actually 2.

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BibTeX entry

@article{Muller2013,
	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 then shows that it actually coincides with the oval. Here we give another proof. We describe the oval by a possibly high degree polynomial, and then show that the degree is actually 2.},
	author = {M{\"{u}}ller, Peter},
	month = {nov},
	pages = 2,
	title = {Another Proof of Segre's Theorem about Ovals},
	url = {http://arxiv.org/abs/1311.3082 http://arxiv.org/pdf/1311.3082v1},
	year = 2013,
	archivePrefix = {arXiv},
	eprint = {1311.3082},
	primaryClass = {math.NT},
	urldate = {2015-09-29}
}