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.
Highlights
We study the connection of Heronian triangles with the problem of the existence of rational cuboids
The example of the rectangular tetrahedron is given, which has lengths of one side irrational and the other integer, but the area of the base is integer
Summary
Autoriai [2] darbe nagrinėjo Herono trikampių ryšį su kol kas neišspręsta racionaliųjų kuboidų egzistavimo problema. Kad racionaliųjų kuboidų egzistavimas yra ekvivalentus stačiakampio tetraedro, kurio visos briaunos prie pagrindinės viršūnės yra racionalieji skaičiai, o pagrindas yra racionalusis Herono trikampis, egzistavimui. Nagrinėjimui autoriai taiko tik elementariosios algebros ir geometrijos faktus, todėl tokie tyrinėjimai gali būti gera medžiaga įvairiems projektiniams darbams su matematikai gabiais mokiniais
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