TY - BOOK ID - 8286278 TI - Geometry revealed : a Jacob's ladder to modern higher geometry PY - 2010 SN - 3540709967 3540709975 PB - New York : Springer, DB - UniCat KW - Geometry, Differential. KW - Geometry. KW - Mathematics. KW - Geometry, Differential KW - Mathematics KW - Geometry KW - Physical Sciences & Mathematics KW - Geometry, Modern. KW - Modern geometry KW - Dynamics. KW - Ergodic theory. KW - Convex geometry. KW - Discrete geometry. KW - Differential geometry. KW - History. KW - Combinatorics. KW - History of Mathematical Sciences. KW - Convex and Discrete Geometry. KW - Differential Geometry. KW - Dynamical Systems and Ergodic Theory. KW - Sphere KW - Discrete groups. KW - Global differential geometry. KW - Differentiable dynamical systems. KW - Combinatorics KW - Algebra KW - Mathematical analysis KW - Groups, Discrete KW - Infinite groups KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Differential equations KW - Global analysis (Mathematics) KW - Topological dynamics KW - Euclid's Elements KW - Discrete mathematics KW - Convex geometry . KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Differential geometry KW - Combinatorial geometry KW - Annals KW - Auxiliary sciences of history KW - Math KW - Science UR - https://www.unicat.be/uniCat?func=search&query=sysid:8286278 AB - 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 t he 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. ER -