Cargando…

An Axiomatic Approach to Geometry Geometric Trilogy I /

Focusing 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 ge...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Borceux, Francis (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edición:1st ed. 2014.
Temas:
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-319-01730-3
003 DE-He213
005 20220115235226.0
007 cr nn 008mamaa
008 131031s2014 sz | s |||| 0|eng d
020 |a 9783319017303  |9 978-3-319-01730-3 
024 7 |a 10.1007/978-3-319-01730-3  |2 doi 
050 4 |a QA440-699 
072 7 |a PBM  |2 bicssc 
072 7 |a MAT012000  |2 bisacsh 
072 7 |a PBM  |2 thema 
082 0 4 |a 516  |2 23 
100 1 |a Borceux, Francis.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 3 |a An Axiomatic Approach to Geometry  |h [electronic resource] :  |b Geometric Trilogy I /  |c by Francis Borceux. 
250 |a 1st ed. 2014. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a XV, 403 p. 288 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
505 0 |a Introduction -- 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 |a Focusing 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 |a Geometry. 
650 0 |a Mathematics. 
650 0 |a History. 
650 0 |a Projective geometry. 
650 1 4 |a Geometry. 
650 2 4 |a History of Mathematical Sciences. 
650 2 4 |a Projective Geometry. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319017297 
776 0 8 |i Printed edition:  |z 9783319017310 
776 0 8 |i Printed edition:  |z 9783319347516 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-01730-3  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713)