In Number Theory, Logic, and Cryptography

Perfect Cuboid


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://www.christianboyer.com/eulerbricks/

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

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


You can check for contributions to this problem on the solutions page.


This web site developed and maintained by

Tim S Roberts

Email: timro21@gmail.com