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OverviewFocusing 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 tosee 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! Full Product DetailsAuthor: Francis BorceuxPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: Softcover reprint of the original 1st ed. 2014 Dimensions: Width: 15.50cm , Height: 2.20cm , Length: 23.50cm Weight: 6.321kg ISBN: 9783319347516ISBN 10: 3319347519 Pages: 403 Publication Date: 23 August 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsIntroduction.- 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.ReviewsFrom 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) 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) Author InformationFrancis 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. Tab Content 6Author Website:Countries AvailableAll regions |
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