| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 11012913 | Journal of Number Theory | 2019 | 6 Pages |
Abstract
A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area. In the proof, we determine the set of rational points on a certain hyperelliptic curve by a standard but sophisticated argument which is based on the 2-descent on its Jacobian variety and Coleman's theory of p-adic abelian integrals.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yoshinosuke Hirakawa, Hideki Matsumura,