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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)

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
Creator
Contributor
Author
Subject
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, 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!
Member of
Cataloging source
IT-FiEUI
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-01730-3
Instantiates
Publication
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.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
Control code
978-3-319-01730-3
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, non-commercial 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
10.1007/978-3-319-01730-3
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-01730-3
Publication
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.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
Control code
978-3-319-01730-3
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, non-commercial 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
10.1007/978-3-319-01730-3
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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