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008 | 160915s2014 gw | s |||| 0|eng d | ||
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_a9783319017303 _9978-3-319-01730-3 |
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024 | 7 |
_a10.1007/978-3-319-01730-3 _2doi |
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_aSpringer _cSpringer _dRU-ToGU |
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_aPBM _2bicssc |
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_aMAT012000 _2bisacsh |
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_a516 _223 |
100 | 1 |
_aBorceux, Francis. _eauthor. _9448012 |
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245 | 1 | 3 |
_aAn Axiomatic Approach to Geometry _helectronic resource _bGeometric Trilogy I / _cby Francis Borceux. |
260 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2014. |
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300 |
_aXV, 403 p. 288 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |
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650 | 0 |
_aGeometry. _9303683 |
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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 |
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773 | 0 | _tSpringer eBooks | |
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-319-01730-3 |
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999 | _c399917 |