An Axiomatic Approach to Geometry

Geometric Trilogy I

Authors: Borceux, Francis

  • Focuses on historical aspects 
  • Supports contemporary approaches of the three aspects of axiomatic geometry: Euclidean, non-Euclidean and projective
  • Includes full solutions to all famous historical problems of classical geometry and hundreds of figures
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eBook 79,72 €
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  • ISBN 978-3-319-01730-3
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Hardcover 94,99 €
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  • ISBN 978-3-319-01729-7
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Softcover 94,99 €
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  • ISBN 978-3-319-34751-6
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About this book

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!

About the authors

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

Reviews

From the book reviews:

“The axiomatic approach to geometry accounts for much of its history and controversies, and this book beautifully discusses various aspects of this. … I thoroughly enjoyed this book, and highly recommend it for instructors who are preparing courses in this material or who just want a great reference on their shelves. … There are exercises and problems appearing at the end of each chapter … . Any decent college library should own this book … .” (Mark Hunacek, MAA Reviews, January, 2014)

“This book is eminently suitable for prospective teachers and their docents. The reader benefits from the author’s long experience in lecturing geometry. The text is presented with contemporary mathematical rigor and free of strenuous historical sources … . This wonderful book offers a deep insight into the beginning of geometric science 35 centuries before, into its further synthetic development through the ages, and into its culmination with Hilbert.” (Rolf Riesinger, zbMATH, Vol. 1298, 2014)


Table of contents (8 chapters)

Buy this book

eBook 79,72 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-01730-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 94,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-01729-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 94,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-319-34751-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Axiomatic Approach to Geometry
Book Subtitle
Geometric Trilogy I
Authors
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-01730-3
DOI
10.1007/978-3-319-01730-3
Hardcover ISBN
978-3-319-01729-7
Softcover ISBN
978-3-319-34751-6
Edition Number
1
Number of Pages
XV, 403
Number of Illustrations and Tables
288 b/w illustrations
Topics