Gamma: Exploring Euler's Constant (Princeton Science Library)

Gamma: Exploring Euler's Constant (Princeton Science Library)

<p>Among the many constants that appear in mathematics, <i>Ï€</i>, <i>e</i>, and <i>i</i> are the most familiar. Following closely behind is <i>y</i>, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.</p><br><p> 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.</p><br><p> 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/<i>n</i>, minus the natural logarithm of <i>n</i>--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues <i>Ï€</i> and <i>e</i>, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.</p><br><p> 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!).</p><br><p> Sure to be popular with not only students and instructors but all math aficionados, <i>Gamma</i> takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.</p>