Author | Aigner, Martin. author |
---|---|
Title | Proofs from THE BOOK [electronic resource] / by Martin Aigner, Gรผnter M. Ziegler |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-04315-8 |
Descript | VIII, 215 p. 198 illus., 6 illus. in color. online resource |
Number Theory -- 1. Six proofs of the infinity of primes -- 2. Bertrandโs 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. Hilbertโs third problem: decomposing polyhedra -- 8. Lines in the plane and decompositions of graphs -- 9. The slope problem -- 10. Three applications of Eulerโs formula -- 11. Cauchyโs rigidity theorem -- 12. Touching simplices -- 13. Every large point set has an obtuse angle -- 14. Borsukโs conjecture -- Analysis -- 15. Sets, functions, and the continuum hypothesis -- 16. In praise of inequalities -- 17. A theorem of Pรณlya on polynomials -- 18. On a lemma of Littlewood and Offord -- 19. Cotangent and the Herglotz trick -- 20. Buffonโs needle problem -- Combinatorics -- 21. Pigeon-hole and double counting -- 22. Three famous theorems on finite sets -- 23. Lattice paths and determinants -- 24. Cayleyโs formula for the number of trees -- 25. Completing Latin squares -- 26. The Dinitz problem -- Graph Theory -- 27. Five-coloring plane graphs -- 28. How to guard a museum -- 29. Turรกnโs graph theorem -- 30. Communicating without errors -- 31. Of friends and politicians -- 32. Probability makes counting (sometimes) easy -- About the Illustrations