Article ID Journal Published Year Pages File Type
4595021 Journal of Number Theory 2008 12 Pages PDF
Abstract

This paper discusses tetrahedra with rational edges forming a geometric progression, focussing on whether they can have rational volume or rational face areas. We examine the 30 possible configurations of such tetrahedra and show that no face of any of these has rational area. We show that 28 of these configurations cannot have rational volume, and in the remaining two cases there are at most six possible examples, and none have been found.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory