000 03773nam a22005295i 4500
001 978-3-540-70997-8
003 DE-He213
005 20140220084520.0
007 cr nn 008mamaa
008 100721s2010 gw | s |||| 0|eng d
020 _a9783540709978
_9978-3-540-70997-8
024 7 _a10.1007/978-3-540-70997-8
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBerger, Marcel.
_eauthor.
245 1 0 _aGeometry Revealed
_h[electronic resource] :
_bA Jacob's Ladder to Modern Higher Geometry /
_cby Marcel Berger.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXII, 860p. 666 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPoints and lines in the plane -- Circles and spheres -- The sphere by itself: can we distribute points on it evenly? -- Conics and quadrics -- Plane curves -- Smooth surfaces -- Convexity and convex sets -- Polygons, polyhedra, polytopes -- Lattices, packings and tilings in the plane -- Lattices and packings in higher dimensions -- Geometry and dynamics I: billiards -- Geometry and dynamics II: geodesic flow on a surface.
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 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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aCombinatorics.
650 0 _aGeometry.
650 0 _aDiscrete groups.
650 0 _aGlobal differential geometry.
650 0 _aMathematics_$xHistory.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aHistory of Mathematics.
650 2 4 _aConvex and Discrete Geometry.
650 2 4 _aDifferential Geometry.
650 2 4 _aCombinatorics.
650 2 4 _aDynamical Systems and Ergodic Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540709961
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-70997-8
912 _aZDB-2-SMA
999 _c111207
_d111207