The problem of finding such a cuboid is also called the brick problem, diagonals problem, perfect box problem, perfect cuboid problem, or rational cuboid ...
mathworld.wolfram.com/PerfectCuboid.html mathworld.wolfram.com/PerfectCuboid.html
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Euler brick - Wikipedia, the free encyclopedia
In mathematics, an Euler brick , named after Leonhard Euler, is a cuboid whose edges and face diagonals are all integers. A primitive Euler brick is an Euler brick whose edges are relatively prime...
en.wikipedia.org/wiki/Euler_brick
Sep 17, 2003 ... A perfect cuboid is a rectangular box whose sides, face diagonals, and space diagonals ... It is not known whether a perfect cuboid exists. ...
www.stetson.edu/~efriedma/papers/unsolved.ppt
Posted: Thu, 27 Dec 2007 16:59:31 UTC Post subject: The Perfect Cuboid Problem ... If this can be proved, it's relatively straightforward to prove that no perfect cuboid exists. I've been sitting at the computer for the past few days, doing exhaustive searches on possible cuboids and the above theorem seems to hold,
www.sosmath.com/CBB/viewtopic.php?t=34818&sid=7517a1b16... www.sosmath.com/CBB/viewtopic.php?t=34818&sid=7517a1b1671020ff9ee2635f6176f9df
It is unknown as to whether there is a perfect cuboid, although many examples are known that satisfy all but one of those conditions [2]. A more general question, also open, asks whether there is a nondegenerate parallelepiped with integer-length edges, face diagonals, and body diagonals [2]. In terms of vectors,
ww2.lafayette.edu/~reiterc/nt/fnpp/fnpp_pp.pdf
This deceptively simple-sounding problem is known as the Perfect Cuboid Problem (among other names). ... One near miss is the cuboid that has edges with lengths 44, 117, and 240, and diagonals with lengths 125, 244, and 267.
www.billthelizard.com/2009/11/unsolved-perfect-cuboid-p... www.billthelizard.com/2009/11/unsolved-perfect-cuboid-problem.html
Perfect Cuboids and Perfect Square Triangles. FLORIAN LUCA. Fakultät Mathematik. Universität Bielefeld. Postfach 10 01 31. 33 501 Bielefeld. Germany ...
www.jstor.org/stable/2690822
A little bit about the Perfect Cuboid ... The Perfect Box as its known, is a box whose edges are all integers, whose face diagonals are integers and it's body diagonal is an integer also. No one has yet found a Perfect Box, but no one has yet proven that it can't exist.
www.beautifulandes.com/PerfectBox.html www.beautifulandes.com/PerfectBox.html
Welcome to "Beautiful Andes" ... Read about one of my favorite unsolved math problems, The Perfect Cuboid; ... Perfect Box...
www.beautifulandes.com/
See Euler Brick ... © 1996-9 Eric W. Weisstein ; 1999-05-26...
www.math.sdu.edu.cn/mathency/math/p/p235.htm
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