The Area of the Medial Parallelogram of a Tetrahedron

Details The Area of the Medial Parallelogram of a Tetrahedron The Area of the Medial Parallelogram of a Tetrahedron

1998-09-01

arxiv.org/abs/math/9809007v1

Mathematics

Metric Geometry

LaTeX (5 pages) 2 figures in LaTeX picture code

Scientific paper

When a pair of non-incident edges of a tetrahedron is chosen, the midpoints of the remaining 4 edges are the vertices of a planar parallelogram. A formula is given in terms of the six edge lengths for the area of this parallelogram. It is not claimed that this formula is new, but it is certainly not well-known. The author would be very grateful for a citation to an occurence of the formula in previously existing literature (by e-mail to dyetter@math.ksu.edu). The result is of some current interest due to the work of Barbieri and Barrett/Crane on attempts to formulate simplicial versions of quantum gravity.

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