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AMS Chelsea Publishing Ser.: Geometria i wyobraźnia S. Cohn-Vossen i–
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Nr przedmiotu eBay: 145155041812
Parametry przedmiotu
- Stan
- ISBN
- 9780821819982
- Subject Area
- Mathematics
- Publication Name
- Geometry and the Imagination
- Publisher
- American Mathematical Society
- Item Length
- 9.1 in
- Subject
- Geometry / General
- Publication Year
- 1999
- Series
- Ams Chelsea Publishing Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Weight
- 23.2 Oz
- Item Width
- 5.9 in
- Number of Pages
- 357 Pages
O tym produkcie
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
0821819984
ISBN-13
9780821819982
eBay Product ID (ePID)
920274
Product Key Features
Number of Pages
357 Pages
Publication Name
Geometry and the Imagination
Language
English
Subject
Geometry / General
Publication Year
1999
Type
Textbook
Subject Area
Mathematics
Series
Ams Chelsea Publishing Ser.
Format
Hardcover
Dimensions
Item Weight
23.2 Oz
Item Length
9.1 in
Item Width
5.9 in
Additional Product Features
Edition Number
2
Intended Audience
College Audience
LCCN
99-015535
Dewey Edition
21
Series Volume Number
87
Illustrated
Yes
Dewey Decimal
516.9
Original Language
German
Table Of Content
The simplest curves and surfaces; Regular systems of points; Projective configurations; Differential geometry; Kinematics; Topology; Index.
Synopsis
Suitable for beginners and experienced mathematicians, this book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. It offers a discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way., This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ''Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books., This remarkable book has endured as a true masterpiece of mathematical expostion. There are few mathematics books that are still so widely read and continue to have so much to offer-even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. "Hilbert and Cohn-Vossen" is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\Bbb{R}3$ In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is "Projective Configurations". In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the "pantheon" of great mathematics books.
LC Classification Number
QA685.H515 1999
Opis przedmiotu podany przez sprzedawcę
Informacje o firmie
South Saxon Books
Steve Rome
, NJ
United States
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- i***2 (2490)- Opinie wystawione przez kupującego.Ostatni miesiącZakup potwierdzonyThis is a great book. Full of history. Excellent eBay seller.
- d***0 (20)- Opinie wystawione przez kupującego.Ostatni miesiącZakup potwierdzonyFast shipping. A little bit of damage water damage and staining in the book.
- d***0 (20)- Opinie wystawione przez kupującego.Ostatni miesiącZakup potwierdzonyGreat seller, fast shipping
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