The Mathematical Mechanic.
THE MATHEMATICAL MECHANIC. Mark Levi. Princeton University Press, 41 William St., Princeton, NJ 08540. 2009. 196 pages. $19.95. ISBN 978-0-691-14020-9.
There are many physical systems that work in two directions. If you apply electric power to a motor, you get shaft power. Apply shaft power to a very similar device and you generate electricity. So it can be at times with mathematics and the physical sciences. At least that is how it appears in The Mathematical Mechanic. The author, Mark Levi, a professor of mathematics at Pennsylvania State University, subtitles his book "Using Physical Reasoning to Solve Problems." The problems in question are mathematical. Levi's first case demonstrates how a fish tank with a right-triangular cross-section is a physical system embodying the Pythagorean theorem and also how it implies the law of sines. Topics increase in mathematical complexity as the book progresses to encompass dozens of examples including a derivation of the Euler-Lagrange equation, heat flow and analytic functions, and a bicycle wheel and the Gauss-Bonnet theorem.