Rational cuboids and Heron triangles II

Rational cuboids and Heron triangles II

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 rectang...

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Veröffentlicht in:Lietuvos matematikos rinkinys 2019-12, Vol.60 (B), p.34-38
Hauptverfasser: Mazėtis, Edmundas, Melničenko, Grigorijus
Format: Artikel
Sprache:eng
Schlagworte:
Euler brick
Heronian triangles
perfect cuboid
rational cuboid
right-angled-vertex tetrahedron
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Beschreibung
Zusammenfassung: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.  
ISSN:0132-2818
2335-898X
DOI:10.15388/LMR.B.2019.15233