MathDB
tetrahedron included in a region

Source: bmo 1988

April 23, 2007
geometry3D geometrytetrahedrongeometry proposed

Problem Statement

Let ABCDABCD be a tetrahedron and let dd be the sum of squares of its edges' lengths. Prove that the tetrahedron can be included in a region bounded by two parallel planes, the distances between the planes being at most d23\frac{\sqrt{d}}{2\sqrt{3}}
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