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Blood Vessel Branching: Beyond the Standard Calculus Problem

by John A. Adam (Old Dominion University)

Year of Award: 2012

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 84, 2011, pp. 196-207

Summary: The author first lays the groundwork by discussing the underlying biological setting, specifying his simplifying assumptions, and introducing some necessary equations from fluid dynamics. He then develops a sequence of models for blood vessel branching based upon a series of ever more comprehensive "cost functionals." The most sophisticated of these models implies certain empirical laws for vascular branching proposed by Wilhelm Roux in 1878, and also yields estimates for the total length of the vascular system.

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About the Author: (From the MathFest 2012 Prizes and Awards Booklet)

John Adam is Professor of Mathematics at Old Dominion University. He received his Ph.D. in theoretical astrophysics from the University of London in 1975. He is author of approximately 100 papers in several areas of applied mathematics and mathematical modeling. His first book, Mathematics in Nature: Modeling Patterns in the Natural World, was published in 2003 by Princeton University Press (paperback in 2006). He enjoys spending time with his family, especially his (thus far) five grandchildren, walking, nature photography, and is a frequent contributor to the Earth Science Picture of the Day (EPOD:

In 2007 he was a recipient of the State Council of Higher Education of Virginia's Outstanding Faculty Award. He co- authored Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin, published by Princeton University Press in 2008. More recently he has authored A Mathematical Nature Walk (2009, paperback version in 2011) and X and the City: Modeling Aspects of Urban Life (2012), both published by Princeton.

Subject classification(s): Applied Mathematics | Mathematical Biology | Mathematical Physics
Publication Date: 
Tuesday, August 7, 2012