Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We discover suprising connections between three seemingly different problems: finding right triangles with rational sides in a non-Euclidean geometry, finding three integers such that the difference of the squares of any two is a square, and the problem of finding rational points on an algebraic surface in algebraic geometry. We will also reinterpret Euler's work on the second problem with a modern point of view.
11 pages, 1 figure

Keywords

Number Theory, Algebraic Geometry, 11D (primary) 11G, 14G, 14J (secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/114060

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606700
 http://arxiv.org/abs/math/0606700

Collections

arXiv