Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0606700,
title = {Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on K3 surfaces},
author = {Robin Hartshorne and Ronald van Luijk},
journal= {arXiv preprint arXiv:math/0606700},
year = {2007}
}
Comments
11 pages, 1 figure