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Viser: Jacob's Ladder of Differential Geometry
Geometry Revealed Vital Source e-bog
Marcel Berger og Lester J. Senechal
om ca. 15 hverdage
Detaljer Om Varen
- Vital Source E-book
- Udgiver: Springer Nature (Juli 2010)
- ISBN: 9783540709978
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Detaljer Om Varen
- 1. Udgave
- Hardback: 872 sider
- Udgiver: Springer London, Limited (August 2010)
- Forfattere: Marcel Berger og Lester J. Senechal
- ISBN: 9783540709961
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended...
In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations.
Marcel Berger is the author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.
I: billiards. - Geometry and dynamics
II: geodesic flow on a surface.