Rational cuboids and Geron triangles - Mazėtis, Edmundas; Melničenko, Grigorijus (Lietuvos matematikos rinkinys, 2018)
The problem of existence of rational cuboids is considered in the article. Equivalent statements ofthis problem are obtained which lead to the existence of Heron’s triangles whose lengths are integralsquares and satisfy other additional conditions. Also, the connections between Euler bricks and theHeron triangles are obtained, which correspond to additional conditions.
Keywords: Heronian triangle; rational cuboid; perfect cuboid; Euler brick