Proofs from the Book

by Aigner, Martin

• ISBN13: 9783540678656
• ISBN10: 3540678654
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-12-01
• Publisher: SPRINGER VERLAG INC

Summary

A collection of proofs in honor or Paul Erdos, whose work included the mathematical approximation of The Book. Offers examples of selection of proofs that the editors consider proofs from the book, based on Erdos's work. Includes a number of illustrations.

Table of Contents

Number Theory	1	(36)
Six proofs of the infinity of primes	3	(4)
Bertrand's postulate	7	(6)
Binomial coefficients are (almost) never powers	13	(4)
Representing numbers as sums of two squares	17	(6)
Every finite division ring is a field	23	(4)
Some irrational numbers	27	(10)
Geometry	37	(48)
Hilbert's third problem: decomposing polyhedra	39	(8)
Lines in the plane and decompositions of graphs	47	(6)
The slope problem	53	(6)
Three applications of Euler's formula	59	(6)
Cauchy's rigidity theorem	65	(4)
Touching simplices	69	(4)
Every large point set has an obtuse angle	73	(6)
Borsuk's conjecture	79	(6)
Analysis	85	(44)
Sets, functions, and the continuum hypothesis	87	(12)
In praise of inequalities	99	(8)
A theorem of Polya on polynomials	107	(8)
On a lemma of Littlewood and Offord	115	(4)
Cotangent and the Herglotz trick	119	(6)
Buffon's needle problem	125	(4)
Combinatorics	129	(44)
Pigeon-hole and double counting	131	(12)
Three famous theorems on finite sets	143	(6)
Lattice paths and determinants	149	(6)
Cayley's formula for the number of trees	155	(6)
Completing Latin squares	161	(6)
The Dinitz problem	167	(6)
Graph Theory	173	(39)
Five-coloring plane graphs	175	(4)
How to guard a museum	179	(4)
Turan's graph theorem	183	(6)
Communicating without errors	189	(10)
Of friends and politicians	199	(4)
Probability makes counting (sometimes) easy	203	(9)
About the Illustrations	212	(1)
Index	213