The Resource An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource)
An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource)
Resource Information
The item An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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, nonEuclidean 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 twobytwo 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 nonEuclidean 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!
 Language
 eng
 Extent
 XV, 403 pages 288 illustrations
 Contents

 Introduction
 Preface
 1.The Prehellenic Antiquity
 2.Some Pioneers of Greek Geometry
 3.Euclid's Elements
 4.Some Masters of Greek Geometry
 5.PostHellenic Euclidean Geometry
 6.Projective Geometry
 7.NonEuclidean Geometry
 8.Hilbert's Axiomatics of the Plane
 Appendices: A.Constructibily
 B.The Three Classical Problems
 C.Regular Polygons
 Index
 Bibliography
 Isbn
 9783319017303
 Label
 An Axiomatic Approach to Geometry : Geometric Trilogy I
 Title
 An Axiomatic Approach to Geometry
 Title remainder
 Geometric Trilogy I
 Statement of responsibility
 by Francis Borceux
 Language
 eng
 Summary
 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, nonEuclidean 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 twobytwo 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 nonEuclidean 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!
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 Borceux, Francis
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Geometry
 Label
 An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Introduction  Preface  1.The Prehellenic Antiquity  2.Some Pioneers of Greek Geometry  3.Euclid's Elements  4.Some Masters of Greek Geometry  5.PostHellenic Euclidean Geometry  6.Projective Geometry  7.NonEuclidean Geometry  8.Hilbert's Axiomatics of the Plane  Appendices: A.Constructibily  B.The Three Classical Problems  C.Regular Polygons  Index  Bibliography
 Control code
 9783319017303
 Dimensions
 unknown
 Extent
 XV, 403 pages 288 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319017303
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319017303
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086454225
 Label
 An Axiomatic Approach to Geometry : Geometric Trilogy I, by Francis Borceux, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Introduction  Preface  1.The Prehellenic Antiquity  2.Some Pioneers of Greek Geometry  3.Euclid's Elements  4.Some Masters of Greek Geometry  5.PostHellenic Euclidean Geometry  6.Projective Geometry  7.NonEuclidean Geometry  8.Hilbert's Axiomatics of the Plane  Appendices: A.Constructibily  B.The Three Classical Problems  C.Regular Polygons  Index  Bibliography
 Control code
 9783319017303
 Dimensions
 unknown
 Extent
 XV, 403 pages 288 illustrations
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319017303
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319017303
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086454225
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