Geometric Trilogy

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  • Geometric Trilogy Book Detail

  • Author : Francis Borceux
  • Release Date : 2013-11-09
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 1350
  • ISBN 13 : 9783319018041
  • File Size : 80,80 MB

Geometric Trilogy by Francis Borceux PDF Summary

Book Description: The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geometry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves. The introduction of differential calculus during the eighteenth century allows widening considerably the range of curves and surfaces considered. The notion of curvature –under multiple forms -- imposes itself as an essential tool for studying the properties of curves and surfaces. And a keen study of some geometrical properties of surfaces gives rise to the theory of algebraic topology. This trilogy is of interest to all those who have to teach or study geometry and need to have a good global overview of the numerous facets of this fascinating topic. It provides both the intuitive and the technical ingredients needed to find one’s way through Euclidean, non-Euclidean, projective, algebraic or differential geometry at a high level.

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Geometric Trilogy

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File Size : 17,17 MB
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The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas

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This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It

An Algebraic Approach to Geometry

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This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natura

An Axiomatic Approach to Geometry

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Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systemati

Manifolds and Differential Geometry

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Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and s