An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally
History and Overview
2007-05-23 v1 Metric Geometry
Abstract
This is an English translation from the Latin original of Leonhard Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur''. In this paper, Euler proves that there exist triangles with integer length sides such that the length of the bisectors of the sides to the opposite angles are integer valued, and he gives a general method for making a certain class of such triangles.
Cite
@article{arxiv.math/0503052,
title = {An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally},
author = {Leonhard Euler},
journal= {arXiv preprint arXiv:math/0503052},
year = {2007}
}
Comments
6 pages, seems to be first English translation of Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur'', Memoires de l'Academie Imperiale des Sciences de St.-Petersbourg 2 (1810), 10-16