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

Proof:
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.

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?

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.
https://github.com/renyxadarox/sheron/b ... n/sheron.c

Nothing revolutionary, just more smart method of generating Heronian triangles using Leonard Euler method

https://github.com/renyxadarox/sheron/b ... sheron2.py