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.
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More From: The American mathematical monthly : the official journal of the Mathematical Association of America
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