Proofs from THE BOOK

"Proofs from THE BOOK" is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps all of the most elegant proofs of mathematical theorems. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book."

"Proofs from THE BOOK" contains 32 different sections, each devoted to one theorem but often containing multiple proofs and related results. It spans a broad range of mathematical fields: number theory, geometry, analysis, combinatorics and graph theory. Erdős himself made many suggestions for the book, but died before its publication. The book is illustrated by Karl Heinrich Hofmann. It has gone through three editions in English, and has also been translated into Persian, French, German, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Russian and Spanish. Additional translations into Korean and Turkish are in preparation.

The proofs include:
*Proof of Bertrand's postulate
*Proof that e is irrational (also showing the irrationality of certain related numbers)
* Five proofs of the infinitude of the primes, including Euclid's and Furstenberg's.

References

*cite book | author=Aigner, Martin; Ziegler, Günter | title=Proofs from THE BOOK | publisher=Springer | location=Berlin; New York | year=2003 | id=ISBN 3-540-40460-0
* [http://www.math.tu-berlin.de/~ziegler/#Publications:Proofs Günter M. Ziegler's homepage] , including a list of editions and translations.
*Citation|last=Shepard|first=Mary|url=http://www.maa.org/reviews/thebook.html|publisher=Mathematical Association of America|title=Read This! Review of Proofs from THE BOOK|year=1999.


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