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.
[sub-project] Heronian Triangles with Square Sides
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?
Re: [sub-project] Heronian Triangles with Square Sides
Nothing revolutionary, just more smart method of generating Heronian triangles using Leonard Euler method
https://github.com/renyxadarox/sheron/b ... sheron2.py
https://github.com/renyxadarox/sheron/b ... sheron2.py