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020 _a9783319017303
_9978-3-319-01730-3
024 7 _a10.1007/978-3-319-01730-3
_2doi
035 _ato000542124
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBorceux, Francis.
_eauthor.
_9448012
245 1 3 _aAn Axiomatic Approach to Geometry
_helectronic resource
_bGeometric Trilogy I /
_cby Francis Borceux.
260 _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
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 0 _amathematics.
_9566183
650 0 _aGeometry.
_9303683
650 1 4 _aMathematics.
_9566184
650 2 4 _aGeometry.
_9303683
650 2 4 _aHistory of Mathematical Sciences.
_9296777
650 2 4 _aProjective Geometry.
_9448013
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-01730-3
912 _aZDB-2-SMA
999 _c399917