| Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry Contributor(s): Berger, Marcel (Author), Senechal, Lester J. (Translator) |
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ISBN: 3540709967 ISBN-13: 9783540709961 Publisher: Springer OUR PRICE: $85.45 Product Type: Hardcover - Other Formats Published: August 2010 Annotation: Both modern differential geometry, which lies at the heart of many recent advances in mathematics, from analysis to algebraic geometry and to mathematical physics, and also classical geometry, have been active subjects of research throughout the 20th century. This fact is the underlying motivating concept for the new book of Marcel Berger. The 'ladder' in question is one on which, in the process of solving a problem, the geometer climbs up one rung or successive rungs of increasing abstraction, each time thus obtaining a better view from higher up of the problem and its environment, recalling the 'ladder' in the Old Testament, that angels ascended and descended... Marcel Berger is the author of numerous successful books on geometry, is this book once again is addressed to all students and teachers of mathematics with an affinity for geometry. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Geometry - Analytic - Mathematics | History & Philosophy |
| Dewey: 516.36 |
| LCCN: 2010920837 |
| Physical Information: 1.9" H x 6.4" W x 9.4" (3.05 lbs) 831 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |