Heronian Tetrahedra Are Lattice Tetrahedra
نویسندگان
چکیده
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 R 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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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 120 شماره
صفحات -
تاریخ انتشار 2013