The Resource An axiomatic approach to geometry, Francis Borceux
An axiomatic approach to geometry, Francis Borceux
- 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!
- Language
- eng
- Extent
- 1 online resource (xv, 399 pages)
- Contents
-
- 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 Axiomatization of the Plane
- Appendices: A.Constructibily
- B.The Three Classical Problems
- C.Regular Polygons
- Isbn
- 9783319017303
- Label
- An axiomatic approach to geometry
- Title
- An axiomatic approach to geometry
- Statement of responsibility
- 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, 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!
- Cataloging source
- GW5XE
- Dewey number
- 516
- Illustrations
- illustrations
- Index
- no index present
- LC call number
- QA445
- Literary form
- non fiction
- Nature of contents
- dictionaries
- Series statement
- Geometric trilogy
- Series volume
- I
- Label
- An axiomatic approach to geometry, Francis Borceux
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- http://library.link/vocab/branchCode
-
- net
- Carrier category
- online resource
- Carrier category code
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
- txt
- Content type MARC source
- rdacontent
- Contents
- 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 Axiomatization of the Plane -- Appendices: A.Constructibily -- B.The Three Classical Problems -- C.Regular Polygons
- Control code
- ocn864878479
- Dimensions
- unknown
- Extent
- 1 online resource (xv, 399 pages)
- File format
- unknown
- Form of item
- online
- Isbn
- 9783319017303
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
- c
- Other control number
- 10.1007/978-3-319-01730-3
- Other physical details
- illustrations
- Quality assurance targets
- unknown
- http://library.link/vocab/recordID
- .b31758484
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
-
- (OCoLC)864878479
- springer3319017306
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.deakin.edu.au/portal/An-axiomatic-approach-to-geometry-Francis/UE1MGlgX1WU/" typeof="CreativeWork http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.deakin.edu.au/portal/An-axiomatic-approach-to-geometry-Francis/UE1MGlgX1WU/">An axiomatic approach to geometry, Francis Borceux</a></span> - <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.library.deakin.edu.au/#Deakin%20University%20Library"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.deakin.edu.au/">Deakin University Library</a></span></span></span></span></div>
