Open AccessRational cuboids and Heron triangles II
Author(s) -
Edmundas Mazėtis,
Grigorijus Melničenko
Publication year - 2019
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.b.2019.15233
Subject(s) - cuboid , tetrahedron , irrational number , base (topology) , mathematics , integer (computer science) , combinatorics , connection (principal bundle) , geometry , computer science , mathematical analysis , programming language
We study the connection of Heronian triangles with the problem of the existence of rational cuboids. It is proved that the existence of a rational cuboid is equivalent to the existence of a rectangular tetrahedron, which all sides are rational and the base is a Heronian triangle. Examples of rectangular tetrahedra are given, in which all sides are integer numbers, but the area of the base is irrational. The example of the rectangular tetrahedron is also given, which has lengths of one side irrational and the other integer, but the area of the base is integer.