Today’s Google homepage is a doodle dedicated to the celebrated mathematician Leonhard Euler whose 306th birthday is today. While you may not know a lot about Euler, if you have ever taken a math class you have been exposed to his mathematical contributions. Among his many contributions, he has two numbers named after him- Euler’s Number (in calculus e) and Euler’s Constant (gamma). He is also the man behind ‘ f(x)’ and the use of the Greek letter π. Euler’s contributions do not end here and they have paved the way for today’s leading mathematicians and physicists.
Celebrate Euler’s birthday with some readings from PUP!
1. Dr. Euler’s Fabulous Formula: Cures Many Mathematical Ills by Paul J. Nahin
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler’s Fabulous Formula shares the fascinating story of this groundbreaking formula–long regarded as the gold standard for mathematical beauty–and shows why it still lies at the heart of complex number theory.
This book is the sequel to Paul Nahin’s An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics’ most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.
The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book’s preface: To mathematicians ten thousand years hence, “Euler’s formula will still be beautiful and stunning and untarnished by time.”
Paul J. Nahin is the author of many best-selling popular math books, including An Imaginary Tale, Digital Dice, Chases and Escapes, When Least Is Best, Duelling Idiots and Other Probability Puzzlers, and Mrs. Perkins’s Electric Quilt (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.
2. Gamma: Exploring Euler’s Constant by Julian Havil
Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.
In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma’s place in mathematics.
Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n–the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery–we don’t even know if gamma can be expressed as a fraction.
Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today–the Riemann Hypothesis (though no proof of either is offered!).
Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.
3. Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson
Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s formula is so simple it can be explained to a child. Euler’s Gem tells the illuminating story of this indispensable mathematical idea.
From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V–E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula. Using wonderful examples and numerous illustrations, Richeson presents the formula’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.
Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast.
David S. Richeson is associate professor of mathematics at Dickinson College.