000			02487nam a2200289Ia 4500
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005			20250213164018.0
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020			_a9783662501221 (pbk.) _c€ 59.95
040			_bENG _cIISER-BPR
041			_aENG
082			_a516 _bBER _223rd
100			_aBerger, Marcel _91071
222			_aMathematics
245		0	_aGeometry revealed : _bA Jacob's ladder to modern higher geometry
250			_a1st ed.
260			_aBerlin: _bSpringer-Verlag, _cc2010.
300			_axvi, 831p. : _bill. ; _c24cm
504			_aIncludes selected abbreviations for journal titles, name index, subject index and symbol index.
520			_aBoth 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 isto 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.
650			_aMathematics _92615
650			_aGeometry _92616
942			_cBK _2ddc
942			_2ddc
947			_a5494.4175000000005
948			_a22
999			_c4211 _d4211