Geometry Revealed
A Jacob's Ladder to Modern Higher Geometry
(Sprache: Englisch)
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...
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Klappentext zu „Geometry Revealed “
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.
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.
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.
Inhaltsverzeichnis zu „Geometry Revealed “
Points 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.
Autoren-Porträt von Marcel Berger
Marcel Berger is Ancien Professeur of the University of Paris and emeritus director of research at the Centre National de la Recherche Scientifique (CNRS), from 1979 to 1981 he was president of the French Mathematical Society and from 1985 to 1994 director of the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette.
Bibliographische Angaben
- Autor: Marcel Berger
- 2010, 848 Seiten, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Übersetzer: Lester J. Senechal
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540709967
- ISBN-13: 9783540709961
- Erscheinungsdatum: 02.08.2010
Sprache:
Englisch
Rezension zu „Geometry Revealed “
From the reviews:"The book is a very readable account of several branches of geometry, classical and modern, elementary and advanced. ... Every chapter is extremely interesting and alive. ... The book is rich in ideas, written in an informal style, with no formulae and no unnecessary technical details. ... Every part of this book is interesting and should be accessible to a wide audience of mathematicians. ... Every mathematician will experience great pleasure in reading this book." (Athanase Papadopoulos, Mathematical Reviews, Issue 2011 m)
"The author provides the reader with an enormous amount of detailed information and thus yields deep insight into the various topics. ... All in all an overwhelming book which is a must ... for everyone having sufficient mathematical knowledge." (G. Kowol, Monatshefte für Mathematik, Vol. 164 (2), October, 2011)
"By considering a hierarchy of 'natural' geometrical objects ... it sets out to investigate significant geometrical problems which are either unsolved or were solved only recently. ... it is undoubtedly a major tour de force, and if you really want to gain an idea of where geometry is going in the 21st century, you will find plenty of exquisite material here." (Gerry Leversha, The Mathematical Gazette, Vol. 96 (356), July, 2012)
"'Geometry Revealed' is a massive text of 831 pages which is organized in twelve chapters and which additionally provides indices for names, subjects and symbols ... throughout the author quite carefully lays out the historical perspective. ... a typical chapter starts with an observation or a problem in elementary geometry. Large parts of the text are very accessible, and a reader who likes (mathematical) physics will often get something extra." (Michael Joswig, Zentralblatt MATH, Vol. 1232, 2012)
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