Proofs from THE BOOK
Published on 25. March 1999
Book
Hardback
VIII, 199 pages
978-3-540-63698-4 (ISBN)
Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Reviews / Votes
"...a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another." - Notices of the AMSMore details
Edition
1st ed. 1998. Corr. 2nd printing
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Illustrations
7 colour figures, references, index
Dimensions
Height: 24.2 cm
Width: 19.3 cm
Weight
720 gr
ISBN-13
978-3-540-63698-4 (9783540636984)
DOI
10.1007/978-3-662-22343-7
Schweitzer Classification
Other editions
New editions
Martin Aigner | Günter M. Ziegler
Proofs from THE BOOK
Book
08/2018
6th Edition
Springer
€64.19
Available immediately
Martin Aigner | Gunter M. Ziegler
Proofs from "The Book"
Book
01/2001
2nd Edition
Springer
€22.91
Article exhausted; check for reprint
Content
Number Theory.- 1. Six proofs of the infinity of primes.- 2. Bertrand's postulate.- 3. Binomial coefficients are (almost) never powers.- 4. Representing numbers as sums of two squares.- 5. Every finite division ring is a field.- 6. Some irrational numbers.- Geometry.- 7. Hilbert's third problem: decomposing polyhedra.- 8. Lines in the plane and decompositions of graphs.- 9. The slope problem.- 10. Three applications of Euler's formula.- 11. Cauchy's rigidity theorem.- 12. The problem of the thirteen spheres.- 13. Touching simplices.- 14. Every large point set has an obtuse angle.- 15. Borsuk's conjecture.- Analysis.- 16. Sets, functions, and the continuum hypothesis.- 17. In praise of inequalities.- 18. A theorem of Pólya on polynomials.- 19. On a lemma of Littlewood and Offord.- Combinatorics.- 20. Pigeon-hole and double counting.- 21. Three famous theorems on finite sets.- 22. Cayley's formula for the number of trees.- 23. Completing Latin squares.- 23. The Dinitz problem.- Graph Theory.- 25. Five-coloring plane graphs.- 26. How to guard a museum.- 27. Turán's graph theorem.- 28. Communicating without errors.- 29. Of friends and politicians.- 30. Probability makes counting (sometimes) easy.- About the Illustrations.