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LEADER: 03494nam a22004095a 4500
001 013879529-0
005 20140103192756.0
008 131031s2014 gw | s ||0| 0|eng d
020 $a9783319017303
020 $a9783319017303
020 $a9783319017297
024 7 $a10.1007/978-3-319-01730-3$2doi
035 $a(Springer)9783319017303
040 $aSpringer
050 4 $aQA440-699
072 7 $aPBM$2bicssc
072 7 $aMAT012000$2bisacsh
082 04 $a516$223
100 1 $aBorceux, Francis,$eauthor.
245 13 $aAn Axiomatic Approach to Geometry :$bGeometric Trilogy I /$cby Francis Borceux.
264 1 $aCham :$bSpringer International Publishing :$bImprint: Springer,$c2014.
300 $aXV, 403 p. 288 illus.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
505 0 $aIntroduction -- Preface -- 1.The Prehellenic Antiquity -- 2.Some Pioneers of Greek Geometry -- 3.Euclid’s Elements -- 4.Some Masters of Greek Geometry -- 5.Post-Hellenic Euclidean Geometry -- 6.Projective Geometry -- 7.Non-Euclidean Geometry -- 8.Hilbert’s Axiomatics of the Plane -- Appendices: A. Constructibily -- B. The Three Classical Problems -- C. Regular Polygons -- Index -- Bibliography.
520 $aFocusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition.   Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!
650 20 $aGeometry, Projective.
650 20 $aGeometry.
650 10 $aMathematics.
650 0 $aMathematics.
650 0 $aGeometry.
650 24 $aHistory of Mathematical Sciences.
776 08 $iPrinted edition:$z9783319017297
988 $a20131221
906 $0VEN