Erschienen: 23.08.2016 Abbildung von Borceux | An Axiomatic Approach to Geometry | Softcover reprint of the original 1st ed. 2014 | 2016


An Axiomatic Approach to Geometry

Geometric Trilogy I

lieferbar ca. 10 Tage als Sonderdruck ohne Rückgaberecht

101,64 €

inkl. Mwst.

Softcover reprint of the original 1st ed. 2014 2016. Buch. xv, 403 S. 288 s/w-Abbildungen, Bibliographien. Softcover

Springer. ISBN 978-3-319-34751-6

Format (B x L): 15,5 x 23,5 cm

Gewicht: 640 g

In englischer Sprache


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!


Die 8. Auflage ist wieder auf sechs Bände angelegt. Darin finden sich übersichtlich und in systematischer Gliederung Vertragsmuster aus der Feder erfahrener Experten. Jedem dieser Muster folgen Anmerkungen, mit denen der dem Vertragsentwurf zu Grunde liegende Sachverhalt und die Gründe für die Wahl des spezifischen Formulars erläutert werden.


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