UNSOLVED PROBLEMS

in Number Theory, Logic, and Cryptography

Euler's Brick

An Euler Brick is just a cuboid, or a rectangular box, in which all of the edges (length, depth, and height) have integer dimensions; and in which the diagonals on all three sides are also integers.

So if the length, depth and height are a, b, and c respectively, then a, b, and c are integers, as are the quantities √(a²+b²) and √(b²+c²) and √(c²+a²).

The problem is to find a perfect cuboid, which is an Euler Brick in which the space diagonal, that is, the distance from any corner to its opposite corner, given by the formula √(a²+b²+c²), is also an integer, or prove that such a cuboid cannot exist .

For further information, please see:

[1] http://mathworld.wolfram.com/EulerBrick.html

[2] http://en.wikipedia.org/wiki/Euler_brick

[3] http://f2.org/maths/peb.html

* There are currently 0 proposed solutions on the solutions page.

[ Home ] [ Introduction ] [ What's New? ] [ FAQ ] [ Chromatic Number ] [ Collatz ] [ Dorabella Cipher ] [ Euler's Brick ] [ Goldbach ] [ Legendre ] [ Odd Perfect Number ] [ Riemann Hypothesis ] [ RSA Challenge ] [ Square of Squares ] [ Twin Primes ] [ Voynich Manuscript ] [ Zodiac ] [ Solutions ] [ Math Tuition ]

       Site developed and maintained by Tim Roberts .
       Last modified: January 02, 2009                        v 019