MARC Record from harvard_bibliographic_metadata

LEADER: 03925nam a22004215a 4500
001 014157768-1
005 20141003190221.0
008 111017s2001 xxu| o ||0| 0|eng d
020 $a9781461221029
020 $a9780817642372 (ebk.)
020 $a9781461221029
020 $a9780817642372
024 7 $a10.1007/978-1-4612-2102-9$2doi
035 $a(Springer)9781461221029
040 $aSpringer
050 4 $aQA440-699
072 7 $aMAT012000$2bisacsh
072 7 $aPBM$2bicssc
082 04 $a516$223
100 1 $aTrudeau, Richard J.,$eauthor.
245 14 $aThe Non-Euclidean Revolution :$bWith an Introduction by H.S.M Coxeter /$cby Richard J. Trudeau.
264 1 $aBoston, MA :$bBirkhäuser Boston,$c2001.
300 $aXIV, 270p. 257 illus.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
505 0 $a1 First Things -- The Origin of Deductive Geometry -- ?aterial Axiomatic Systems -- Logic -- Proofs -- A Simple Example of a ?aterial Axiomatic System -- Exercises -- Notes -- 2 Euclidean Geometry -- ?ow ?ig Is a Point? -- Euclid’s Primitive Terms -- Euclid’s Defined Terms (Part 1) -- “Sufficient for Each Day Is the Rigor Thereof” -- Euclid’s Defined Terms (Part 2) -- Euclid’s Axiorns -- Theorems Proven Without Postulate 5 -- Theorems Proven With Postulate 5 -- Index to Euclidean Geometry -- Exercises -- Notes -- 3 Geometry and the Diamond Theory of Truth -- ?ant’s Distinctions -- Synthetic A Priori Statements -- Geometry as Synthetic A Priori -- ?ant’s Doctrine of Space -- The Diamond Theory of Truth -- Notes -- 4 The Problem With Postulate 5 -- Poseidonios -- Proof of Postulate 5, After Poseidonios -- Metageometry -- Evaluation of Poseidonios’ Reorganization -- Overview of Later Attempts -- So Near -- An Experimental Test of Postulate 5 -- Exercises -- Notes -- 5 The Possibility of Non-Euclidean Geometry -- The Logical Possibility of Non-Euclidean Geometry -- The Founders of Non-Euclidean Geometry -- The Psychological Impossibility of Non-Euclidean Geometry -- Formal Axiomatic Systems -- A Simple Example of a Formal Axiomatic System -- How to Not Let the Pictures Bother You -- Exercise -- Notes -- 6 Hyperbolic Geometry -- Hyperbolic Geometry (Part 1) -- Reconciliation With Common Sense -- Hyperbolic Geometry (Part 2) -- Glimpses -- Exercises -- Notes -- 7 Consistency -- Models -- Poincaré’s Model -- Can We Be Sure Euclidean Geometry Is Consistent? -- Notes -- 8 Geometry and the Story Theory of Truth -- Kant Revisited -- The Luneburg—Blank Theory of Visual Space -- The Diamond Theory in Decline -- The Story Theory of Truth -- Notes.
520 $aHow unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.
650 20 $aGeometry.
650 10 $aMathematics.
650 0 $aGeometry.
650 0 $aMathematics.
650 24 $aHistory of Mathematical Sciences.
650 24 $aMathematics, general.
776 08 $iPrinted edition:$z9780817642372
988 $a20140910
906 $0VEN