Download e-book for kindle: An Axiomatic Approach to Geometry: Geometric Trilogy I by Francis Borceux

By Francis Borceux

ISBN-10: 3319017292

ISBN-13: 9783319017297

ISBN-10: 3319347519

ISBN-13: 9783319347516

Focusing methodologically on these old points which are proper to helping instinct in axiomatic methods to geometry, the ebook develops systematic and smooth techniques to the 3 middle points of axiomatic geometry: Euclidean, non-Euclidean and projective. traditionally, axiomatic geometry marks the foundation of formalized mathematical task. it's during this self-discipline that almost all traditionally recognized difficulties are available, the suggestions of that have ended in a variety of almost immediately very lively domain names of study, specially in algebra. the popularity of the coherence of two-by-two contradictory axiomatic platforms for geometry (like one unmarried parallel, no parallel in any respect, a number of parallels) has ended in the emergence of mathematical theories in keeping with an arbitrary method of axioms, an important function of latest mathematics.

This is an engaging ebook for all those that educate or examine axiomatic geometry, and who're drawn to the historical past of geometry or who are looking to see an entire evidence of 1 of the recognized difficulties encountered, yet no longer solved, in the course of their reports: circle squaring, duplication of the dice, trisection of the perspective, building of standard polygons, building of types of non-Euclidean geometries, and so on. It additionally presents countless numbers of figures that aid intuition.

Through 35 centuries of the background of geometry, notice the beginning and stick to the evolution of these leading edge rules that allowed humankind to improve such a lot of points of up to date arithmetic. comprehend some of the degrees of rigor which successively validated themselves in the course of the centuries. Be surprised, as mathematicians of the nineteenth century have been, while staring at that either an axiom and its contradiction could be selected as a sound foundation for constructing a mathematical idea. go through the door of this extraordinary global of axiomatic mathematical theories!

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An Axiomatic Approach to Geometry: Geometric Trilogy I by Francis Borceux

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