LEADER 03579oam 2200445 450 001 9910300145503321 005 20190911112725.0 010 $a3-319-01730-6 024 7 $a10.1007/978-3-319-01730-3 035 $a(OCoLC)869793002 035 $a(MiFhGG)GVRL6UNI 035 $a(EXLCZ)993710000000057971 100 $a20131022d2014 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 13$aAn axiomatic approach to geometry $egeometric trilogy I /$fFrancis Borceux 205 $a1st ed. 2014. 210 1$aCham, Switzerland :$cSpringer,$d2014. 215 $a1 online resource (xv, 403 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a3-319-01729-2 320 $aIncludes bibliographical references and index. 327 $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. 330 $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! 606 $aGeometry 606 $aAxiomatic set theory 615 0$aGeometry. 615 0$aAxiomatic set theory. 676 $a510.9 700 $aBorceux$b Francis$4aut$4http://id.loc.gov/vocabulary/relators/aut$054604 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910300145503321 996 $aAn Axiomatic Approach to Geometry$92512356 997 $aUNINA