Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry

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9783540709961: Geometry Revealed: A Jacob's Ladder to Modern Higher 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 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.

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About the Author:

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.

Review:

“Geometry Revealed is to give the reader a feel for the conceptual frameworks of modern geometry, attempting to reach as far as possible with a minimum of assumed knowledge and formal scaffolding. ... Geometry Revealed being useful for research mathematicians as a still reasonably up-to-date survey. ... Geometry Revealed offered an ascent into the wonders of a new world.” (Danny Yee, Danny Yee’s Book Reviews, dannyreviews.com, July, 2015)

“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)

“The book contains twelve chapters, each of them is a collection of such problems about geometric objects with more and more complexity ... . The chapters are independent from each other, any of them can serve as a course. Researchers in geometry can use it as a source for further research. ... the book is accessible to a wide audience of people who are interested in geometry.” (János Kincses, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)

“‘Geometry Revealed’ is a massive text of 831 pages which is organized in twelve chapters and which additionally provid

es 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)

“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)

“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)

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Marcel Berger (author), Lester J. Senechal (translator)
Editorial: Springer Berlin Heidelberg 2010-08-02, Heidelberg |London (2010)
ISBN 10: 3540709967 ISBN 13: 9783540709961
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Descripción Springer Berlin Heidelberg 2010-08-02, Heidelberg |London, 2010. hardback. Estado de conservación: New. Nº de ref. de la librería 9783540709961

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Descripción Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 2011. Hardback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAW9783540709961

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Marcel Berger, Lester J. Senechal (Translator)
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Descripción Springer, 2010. Hardcover. Estado de conservación: New. 2010. This item is printed on demand. Nº de ref. de la librería DADAX3540709967

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Descripción Springer, 2010. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería M3540709967

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Descripción Springer, 2010. Hardback. Estado de conservación: NEW. 9783540709961 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0343180

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Berger, Marcel
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9783540709961_lsuk

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Descripción Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 2009. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9783540709961

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Descripción Springer-Verlag Gmbh Jan 2011, 2011. Buch. Estado de conservación: Neu. Neuware - 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. 831 pp. Englisch. Nº de ref. de la librería 9783540709961

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Marcel Berger
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Descripción Springer, 2010. Estado de conservación: New. Nº de ref. de la librería L9783540709961

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Descripción Springer-Verlag Gmbh Jan 2011, 2011. Buch. Estado de conservación: Neu. Neuware - 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. 831 pp. Englisch. Nº de ref. de la librería 9783540709961

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