Gamma: Exploring Euler's Constant - Julian Havil [pdf]


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Gamma: Exploring Euler's Constant - Julian Havil [pdf]
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     Gamma, Exploring Euler's Constant - Julian Havil.pdf -
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 							image
  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