## [sub-project] Heronian Triangles with Square Sides

Fehler und Wünsche zum Projekt yoyo@home
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x3mEn
Prozessor-Polier
Beiträge: 101
Registriert: 20.03.2011 22:23

### [sub-project] Heronian Triangles with Square Sides

Abstract
If Perfect cuboid exists, the squares of 3 its face diagonals should construct a Heronian triangle.

Proof:
photo_2021-02-12_10-19-32.jpg (52.76 KiB) 505 mal betrachtet

Note: Heronian triangle is a triangle that has side lengths and area that are all integers.

At the moment it is known about only two Heronian triangles with square sides:
(1853², 4380², 4427², area=32918611718880)
(11789², 68104² , 68595², area=284239560530875680)

The first triangle was probably discovered by Pantelimon Stanica at 2013.
The second triangle was found by Randall L. Rathbun at April 4, 2018.

I propose to beat the record and try to find the 3rd triangle.

fwjmath
XBOX360-Installer
Beiträge: 83
Registriert: 19.10.2010 15:26

### Re: [sub-project] Heronian Triangles with Square Sides

With this expression it is much harder to see how to optimize for an exhaustive search. The different factors may compensate to make a perfect square. Do you have a more concrete idea on how to do that?

x3mEn
Prozessor-Polier
Beiträge: 101
Registriert: 20.03.2011 22:23

### Re: [sub-project] Heronian Triangles with Square Sides

fwjmath hat geschrieben:
23.04.2021 13:57
With this expression it is much harder to see how to optimize for an exhaustive search. The different factors may compensate to make a perfect square. Do you have a more concrete idea on how to do that?
Hi, fwjmath!
Yes, sure.