## Euler BricksApril 26, 2013 You can likely gauge the mathematical precocity of a child by the age at which he or she exhibits knowledge of one of the many things associated with Leonhard Euler. Euler accomplished much in his life, and he was not just an eminent mathematician, but a physicist who made contributions to mechanics and astronomy. A principal scientific contribution was his development of the Huygens wave theory of light as a counterpoint to the corpuscular theory in Newton's Opticks.
in which a, b and c are the lengths of the sides, and d, e and f are the diagonals, as shown in the figure. These must all be integers.
^{10} have been unsuccessful.
There are ten Euler bricks in the range (1 ≤ a ≤ b ≤ c ≤ 1000). These are listed in the table below.
## References:- Eric W. Weisstein, "Euler Brick," from MathWorld--A Wolfram Web Resource.
- Ivars Peterson, "Euler Bricks and Perfect Polyhedra," from Ivars Peterson's MathTrek (October 25, 1999), archived at The Mathematical Association of America web site.
- Oliver Knill, "Treasure Hunting Perfect Euler bricks," Harvard University, February 24, 2009 (PDF File).
- 101 Primitive Pythagorean Triples, Rutgers University Mathematics Department Web Site.
Linked Keywords: Mathematics; mathematical; Leonhard Euler; mathematician; physicist; mechanics; astronomy; Christiaan Huygens; wave theory of light; corpuscular theory; Isaac Newton; Opticks; Basel problem; infinite series formula of pi; Wikimedia Commons; brick; Euler brick; rectangle; rectangular; cuboid; edge; diagonal; integer; Pythagorean triple; set; equation; Inkscape; The On-Line Encyclopedia of Integer Sequences™; shortest edge; intermediate edge; longest edge; brute-force search; coding; computer program; source code; arbitrary-precision arithmetic library; GNU Multiple Precision Arithmetic Library; Plato; Roger Penrose. |
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