Pith. sign in

REVIEW

Rational Right Triangles of a Given Area

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1706.05919 v1 pith:IHFLMO5Q submitted 2017-06-19 math.NT

Rational Right Triangles of a Given Area

classification math.NT
keywords areagivenrighttrianglesgeometricrational-sidedtriangleareas
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
abstract

Starting from any given rational-sided, right triangle, for example the $(3,4,5)$-triangle with area $6$, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show further that the set of all such triangles of a given area is finitely generated under our geometric construction. Such areas are known as "congruent numbers" and have a rich history in which all the results in this article have been proved and far more. Yet, as far as we can tell, this seems to be the first exploration using this kind of geometric technique.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.