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, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-662-22343-7 |
Descript | VIII, 199 p. 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. The problem of the thirteen spheres -- 13. Touching simplices -- 14. Every large point set has an obtuse angle -- 15. Borsukโs conjecture -- Analysis -- 16. Sets, functions, and the continuum hypothesis -- 17. In praise of inequalities -- 18. A theorem of Pรณlya 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. Cayleyโs 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. Turรกnโs graph theorem -- 28. Communicating without errors -- 29. Of friends and politicians -- 30. Probability makes counting (sometimes) easy -- About the Illustrations