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Geometry Revealed A Jacobs Ladder to Modern Higher Geometry pdf

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 Geometry Revealed: A Jacob’s Ladder to Modern Higher Geometry By Marcel Berger
  2010 | 848 Pages |
ISBN: 3540709967 | PDF | 13 MB
  
  
  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.
						

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