Rational cuboids and Heron triangles II
Articles
Edmundas Mazėtis
Vilnius University
https://orcid.org/0000-0001-8604-9179
Grigorijus Melničenko
Vytautas Magnus University
Published 2019-12-05
https://doi.org/10.15388/LMR.B.2019.15233
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Keywords

right-angled-vertex tetrahedron
Heronian triangles
rational cuboid
perfect cuboid
Euler brick

How to Cite

Mazėtis E. and Melničenko G. (2019) “Rational cuboids and Heron triangles II”, Lietuvos matematikos rinkinys, 60(B), pp. 34-38. doi: 10.15388/LMR.B.2019.15233.

Abstract

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.

 

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