Rational cuboids and Geron triangles

The problem of existence of rational cuboids is considered in the article. Equivalent statements of this problem are obtained which lead to the existence of Heron’s triangles whose lengths are integral squares and satisfy other additional conditions. Also, the connections between Euler bricks and t...

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Main Authors:	Edmundas Mazėtis, Grigorijus Melničenko
Format:	Article
Language:	English
Published:	Vilnius University Press 2018-12-01
Series:	Lietuvos Matematikos Rinkinys
Subjects:	Heronian triangle rational cuboid perfect cuboid Euler brick
Online Access:	https://www.journals.vu.lt/LMR/article/view/14987

id	doaj-0513cb52b1b14bcb9cb7ad15d75a54cc
record_format	Article
spelling	doaj-0513cb52b1b14bcb9cb7ad15d75a54cc2020-11-25T03:08:36ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2018-12-0159B10.15388/LMR.B.2018.9Rational cuboids and Geron trianglesEdmundas Mazėtis0Grigorijus Melničenko1Vilnius UniversityVytautas Magnus University The problem of existence of rational cuboids is considered in the article. Equivalent statements of this problem are obtained which lead to the existence of Heron’s triangles whose lengths are integral squares and satisfy other additional conditions. Also, the connections between Euler bricks and the Heron triangles are obtained, which correspond to additional conditions. https://www.journals.vu.lt/LMR/article/view/14987Heronian trianglerational cuboidperfect cuboidEuler brick
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Edmundas Mazėtis Grigorijus Melničenko
spellingShingle	Edmundas Mazėtis Grigorijus Melničenko Rational cuboids and Geron triangles Lietuvos Matematikos Rinkinys Heronian triangle rational cuboid perfect cuboid Euler brick
author_facet	Edmundas Mazėtis Grigorijus Melničenko
author_sort	Edmundas Mazėtis
title	Rational cuboids and Geron triangles
title_short	Rational cuboids and Geron triangles
title_full	Rational cuboids and Geron triangles
title_fullStr	Rational cuboids and Geron triangles
title_full_unstemmed	Rational cuboids and Geron triangles
title_sort	rational cuboids and geron triangles
publisher	Vilnius University Press
series	Lietuvos Matematikos Rinkinys
issn	0132-2818 2335-898X
publishDate	2018-12-01
description	The problem of existence of rational cuboids is considered in the article. Equivalent statements of this problem are obtained which lead to the existence of Heron’s triangles whose lengths are integral squares and satisfy other additional conditions. Also, the connections between Euler bricks and the Heron triangles are obtained, which correspond to additional conditions.
topic	Heronian triangle rational cuboid perfect cuboid Euler brick
url	https://www.journals.vu.lt/LMR/article/view/14987
work_keys_str_mv	AT edmundasmazetis rationalcuboidsandgerontriangles AT grigorijusmelnicenko rationalcuboidsandgerontriangles
_version_	1724665455291924480

Rational cuboids and Geron triangles

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