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Heronian Tetrahedra are Lattice Tetrahedra

by Susan Marshall and Alexander Perlis

Year of Award: 2014

Publication Information: The American Mathematical Monthly, vol. 120, no. 2, February 2013, pp. 140-149.

Summary (adapted from the MAA Prizes and Awards booklet for MathFest 2014):  Heronian triangles are those whose side lengths and area are integer-valued. These seemingly simple objects have long been studied and written about, including a result from this journal by P. Yiu that they can be placed in the plane so the vertices have integer coordinates. In this paper, the authors bring Yiu's result to three dimensions by considering Heronian tetrahedra, those tetrahedra with integer side lengths, face areas and volume.

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About the Authors: (From the MathFest 2014 MAA Prizes and Awards Booklet)

Susan H. Marshall received her B.S. from Wake Forest University in 1993 and her Ph.D. from The University of Arizona in 2001. She currently teaches at Monmouth University and enjoys the beaches and boardwalks of the Jersey Shore with her spouse David and their children Gillian and Dylan.

Alexander R. Perlis received his B.S. from Louisiana State University in 1992 and his Ph.D. from The University of Arizona in 2004. He is currently a systems administrator at Louisiana State University. His interests include nonprofit community bicycle education and community radio, and he enjoys going on walks and listening to Cajun music with his spouse Heather and their child Astrid.


Subject classification(s): Geometry and Topology | Fractal Geometry | Solid Geometry | Polyhedra
Publication Date: 
Wednesday, August 13, 2014