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Heronian Tetrahedra Are Lattice Tetrahedra
Susan H. Marshall and Alexander R. Perlis
The American Mathematical Monthly
Vol. 120, No. 2 (February 2013), pp. 140-149
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.02.140
Page Count: 10
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Abstract Extending a similar result about triangles, we show that each Heronian tetrahedron may be positioned with integer coordinates. More generally, we show the following: if an integral distance set in R3 can be positioned with rational coordinates, then it can in fact be positioned with integer coordinates. The proof, which uses the arithmetic of quaternions, is tantamount to an algorithm.
Copyright the Mathematical Association of America 2013