An Axiomatic Approach to Geometry | Geometric Trilogy I

Francis Borceux

ISBN 10: 3319017292 / ISBN 13: 9783319017297

Verlag: Springer International Publishing, 2013

Beschreibung

An Axiomatic Approach to Geometry | Geometric Trilogy I | Francis Borceux | Buch | xv | Englisch | 2013 | Springer International Publishing | EAN 9783319017297 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.

Bestandsnummer des Verkäufers 105691282

Bibliografische Details

• Titel: An Axiomatic Approach to Geometry | Geometric Trilogy I
• Verlag: Springer International Publishing
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 3319017292
• ISBN-13: 9783319017297
• Einband: Buch
• Zustand: Neu
• Abmessungen: 241B x 160 H x 29 T Millimeter Breite: 241 mm, Höhe: 160 mm, Tiefe: 29 mm
• Gewicht: 793 Gramm
• Verkäuferkataloge:
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Über diesen Titel

Inhaltsangabe

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!

Über die Autorin bzw. den Autor

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.