# The Number [pi]

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This is a clever, beautiful book. The authors trace the thread of $\pi$ through the long history of mathematics. In so doing, they touch upon many major subjects in mathematics: geometry (of course), number theory, Galois theory, probability, transcendental numbers, analysis, and, as their crown jewel, the theory of elliptic functions, which connects many of the other subjects. By this device, the authors provide a tour through mathematics, one that mathematicians of all levels, amateur or professional, may appreciate. In many cases, the tour stops at beloved topics from particular special interest groups. Remarkably, $\pi$ is often found at the places of deepest beauty. Anyone from undergraduate mathematics majors through university professors will find many things to enjoy in this book.Thus, in 1706 he used the formula 7T 1 1 (2.37) a = 4 arctan - a arctan a - to obtain 100 digits for TT. Applying the formula tan 29 = ^^ag twice, one finds / 1\ 5 / 1\ 120 tan 2 arctan - 1 = a and then tan I 4 arctan - I = , \ 5/ 12 y 5J 119 which isanbsp;...

 Title : The Number [pi] Author : Pierre Eymard, Jean Pierre Lafon Publisher : American Mathematical Soc. - 2004

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