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This revised and enlarged fourth edition of "Proofs from THE BOOK" features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improvements and surprises, among them a new proof for "Hilbert's Third Problem". From the Reviews "... Inside PFTB (Proofs from The Book) is indeed 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. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. Moreover, the exposition makes them transparent. ..." LMS Newsletter, January 1999.

Mathematics. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematics - General --- Algebra. --- Math --- Mathematical analysis. --- Analysis (Mathematics). --- Geometry. --- Mathematical logic. --- Number theory. --- Combinatorics. --- Mathematical Logic and Foundations. --- Mathematics, general. --- Number Theory. --- Analysis. --- Science --- Mathematical analysis --- Logic, Symbolic and mathematical. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Combinatorics --- Algebra --- Euclid's Elements --- Number study --- Numbers, Theory of --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Combinatorial analysis. --- 517.1 Mathematical analysis