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001 ocn884616897;

003 OCoLC;

005 20150428113459.0;

008 140725s2014 gw a b 001 0 eng d;

020 a| 9783662442043 (acid-free paper);

020 a| 3662442043 (acid-free paper);

020 z| 9783662442050 (eBook);

020 z| 3662442051 (eBook);

035 a| (Sirsi) 40024552943;

035 a| 40024552943;

035 a| (OCoLC)884616897;

050 4 a| QA36b| .A36 2014;

100 1 a| Aigner, Martin,d| 1942-=| ^A91554;

245 10 a| Proofs from the book /c| Martin Aigner, Günter M. Ziegler ; including illustrations by Karl H. Hofmann.;

250 a| Fifth edition.;

264 1 a| Berlin :b| Springer,c| [2014];

300 a| viii, 308 pages :b| illustrations (some color) ;c| 25 cm;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

504 a| Includes bibliographical references and index.;

505 0 a| Number theory: Six proofs of the infinity of primes ; Bertrand's postulate ; Binomial coefficients are (almost) never powers ; Representing numbers as sums of two squares ; The law of quadratic reciprocity ; Every finite division ring is a field ; The spectral theorem and Hadamard's determinant problem ; Some irrational numbers ; Three times [pi squared]/6 -- Geometry: Hilbert's third problem : decomposing polyhedra ; Lines in the plane and decompositions of graphs ; The slope problem ; Three applications of Euler's formula ; Cauchy's rigidity theorem ; The Borromean rings don't exist ; Touching simplices ; Every large point set has an obtuse angle ; Borsuk's conjecture -- Analysis: Sets, functions, and the continuum hypothesis ; In praise of inequalities ; The fundamental theorem of algebra ; One square and an odd number of triangles ; A theorem of Pólya on polynomials ; On a lemma of Littlewood and Offord ; Cotangent and the Herglotz trick ; Buffon's needle problem -- Combinatorics: Pigeon-hole and double counting ; Tiling rectangles ; Three famous theorems on finite sets ; Shuffling cards ; Lattice paths and determinants ; Cayley's formula for the number of trees ; Identities versus bijections ; The finite Kakeya problem ; Completing Latin squares -- Graph theory: The Dinitz problem ; Permanents and the power of entropy ; Five-coloring plane graphs ; How to guard a museum ; Turán's graph theorem ; Communicating without errors ; The chromatic number of Kneser graphs ; Of friends and politicians ; Probability makes counting (sometimes) easy.;

520 8 a| The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented.;

650 0 a| Mathematics.=| ^A2085;

700 1 a| Ziegler, Günter M.=| ^A363517;

949 i| 30372016577733o| jjlm;

960 o| 1s| 59.99t| Joyner48u| JAPPz| USD;

596 a| 1;

998 a| 3749428;

999 a| QA36 .A36 2014w| LCc| 1i| 30372016577733d| 4/12/2022e| 3/25/2019l| JGESm| JOYNERn| 8q| 1r| Ys| Yt| JGESBKu| 4/10/2015x| BOOKz| JSTACKSo| .STAFF. jjlm;

Proofs from the book / Martin Aigner, Günter M. Ziegler ; including illustrations by Karl H. Hofmann.

Author/creator	Aigner, Martin, 1942-
Other author	Ziegler, Günter M.
Format	Book
Edition	Fifth edition.
Publication	Berlin : Springer, [2014]
Copyright Date	©2014
Description	viii, 308 pages : illustrations (some color) ; 25 cm
Subjects	Mathematics.

Contents	Number theory: Six proofs of the infinity of primes ; Bertrand's postulate ; Binomial coefficients are (almost) never powers ; Representing numbers as sums of two squares ; The law of quadratic reciprocity ; Every finite division ring is a field ; The spectral theorem and Hadamard's determinant problem ; Some irrational numbers ; Three times [pi squared]/6 -- Geometry: Hilbert's third problem : decomposing polyhedra ; Lines in the plane and decompositions of graphs ; The slope problem ; Three applications of Euler's formula ; Cauchy's rigidity theorem ; The Borromean rings don't exist ; Touching simplices ; Every large point set has an obtuse angle ; Borsuk's conjecture -- Analysis: Sets, functions, and the continuum hypothesis ; In praise of inequalities ; The fundamental theorem of algebra ; One square and an odd number of triangles ; A theorem of Pólya on polynomials ; On a lemma of Littlewood and Offord ; Cotangent and the Herglotz trick ; Buffon's needle problem -- Combinatorics: Pigeon-hole and double counting ; Tiling rectangles ; Three famous theorems on finite sets ; Shuffling cards ; Lattice paths and determinants ; Cayley's formula for the number of trees ; Identities versus bijections ; The finite Kakeya problem ; Completing Latin squares -- Graph theory: The Dinitz problem ; Permanents and the power of entropy ; Five-coloring plane graphs ; How to guard a museum ; Turán's graph theorem ; Communicating without errors ; The chromatic number of Kneser graphs ; Of friends and politicians ; Probability makes counting (sometimes) easy.
Summary	The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented.
Bibliography note	Includes bibliographical references and index.
ISBN	9783662442043 (acid-free paper)
ISBN	3662442043 (acid-free paper)

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Library	Location	Call Number	Status	Item Actions
Joyner	General Stacks	QA36 .A36 2014	✔ Available	Place Hold

Proofs from the book / Martin Aigner, Günter M. Ziegler ; including illustrations by Karl H. Hofmann.

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