Most readers of MAA Reviews are surely familiar with the story of young Carl Friedrich Gauss demonstrating his skill at mathematics at about age 10 by rapidly deducing the sum of the integers from 1 to 100 by pairing the numbers off into 50 pairs each totaling 101, and multiplying. That incident serves as the motivation for this collection of similar techniques, each one illustrating a quick shortcut or simplification that can be used to cut seemingly-complex problems down to something more easily solved. These problems are called “Gauss problems,” in an entirely-appropriate bit of author nomenclature.
The book is far-reaching in its search for mathematical dexterity. Examples of the tricks (in the best possible sense of that term) that are illustrated and explained are telescoping series, Pascal’s triangle, Fibonacci numbers, and trigonometric identities that simplify sums. Many of these applications suggest or are drawn from mathematical contest problems, as in “Calculate the product of tan A for A = 1, 2,… 89 degrees.”.
The title Wearing Gauss’s Jersey refers to the author’s basketball jersey, which bears a heptadecagon as an homage to one of Gauss’s earliest discoveries: that this figure is among the 31 odd-sided polygons that can be constructed with straightedge and compass. The book is perhaps best enjoyed in small doses; while the mathematics is insightful and usually quite interesting, there is a lot to process. The payoff is well-worth the effort, even if that effort is expended over time; everyone will likely come away with some new “aha!” insights.
Mark Bollman (firstname.lastname@example.org) is professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. Mark’s claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.