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The Symmetries of Things [Englisch] [Gebundene Ausgabe]

John H. Conway , Heidi Burgiel , Chaim Goodman-Strauss

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Kurzbeschreibung

18. April 2008
Start with a single shape. Repeat it in some way-translation, reflection over a line, rotation around a point-and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

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Wird oft zusammen gekauft

The Symmetries of Things + Regular Algebra and Finite Machines (Dover Books on Mathematics) + Elliptic Tales: Curves, Counting, and Number Theory
Preis für alle drei: EUR 87,10

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Pressestimmen

The book contains many new results. ... [and] is printed on glossy pages with a large number of beautiful full-colour illustrations, which can be enjoyed even by non-mathematicians. -- EMS Newsletter, June 2009 One of the most base concepts of art [is] symmetry. The Symmetries of Things is a guide to this most basic concept showing that even the most basic of things can be beautiful-and addresses why the simplest of patterns mesmerizes humankind and the psychological and mathematical importance of symmetry in ones every day life. The Symmetries of Things is an intriguing book from first page to last, highly recommended to the many collections that should welcome it. -- The Midwest Book Review, June 2008 Conway, Burgiel, and Goodman-Strauss have written a wonderful book which can be appreciated on many levels. ... [M]athematicians and math-enthusiasts at a wide variety of levels will be able to learn some new mathematics. Even better, the exposition is lively and engaging, and the authors find interesting ways of telling you the things you already know in addition to the things you don't. -- Darren Glass, MAA Reviews, July 2008 This rich study of symmetrical things ... prepares the mind for abstract group theory. It gets somewhere, it justifies the time invested with striking results, and it develops ... phenomena that demand abstraction to yield their fuller meaning... the fullest available exposition with many new results. -- D. V. Feldman, CHOICE Magazine , January 2009 This book is a plaything, an inexhaustible exercise in brain expansion for the reader, a work of art and a bold statement of what the culture of math can be like, all rolled into one. Like any masterpiece, The Symmetries of Things functions on a number of levels simultaneously... It is imperative to get this book into the hands of as many young mathematicians as possible. And then to get it into everyone else's hands. -- Jaron Lanier, American Scientist, January 2009 You accompany the authors as they learn about the structures they so beautifully illustrate on over 400 hundred glossy and full-colour pages. Tacitly, you are given an education in the ways of thought and skills of way-finding in mathematics... The style of writing is relaxed and playful ... we see the fusing of the best aspects of textbooks-conciseness, flow, reader-independence-with the best bit of popular writing-accessibility, fun, beauty. -- Phil Wilson, Plus Magazine, February 2009 This book gives a refreshing and comprehensive account of the subject of symmetry-a subject that has fascinated humankind for centuries... Overall, the book is a treasure trove, full of delights both old and new. Much of it should be accessible for anyone with an undergraduate-level background in mathematics, and is likely to stimulate further interest. -- Marston Conder, Mathematical Reviews, March 2009 Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, together with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers. -- L'Enseignement Mathematique, December 2009

Synopsis

Start with a single shape. Repeat it in some way - translation, reflection over a line, rotation around a point - and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

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Amazon.com: 4.3 von 5 Sternen  7 Rezensionen
40 von 43 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Exquisite and fascinating and informative 23. September 2009
Von rbnn - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
Fascinating and thrilling take on finite groups, presented by means of planar and higher-dimensional symmetries.

Presentation will be clear and interesting to laypersons and to mathematicians. Three features distinguish this book from other discussions of symmetry.

First is the inherent interest in the subject. Symmetry is a topic of much greater importance and pervasiveness than most people realize. This book helps us see it in many places we might not think to look, and its classification and analysis is extremely informative and thought-provoking.

Second is the beauty of the examples, which deal with elegant and attractive patterns.

Third is the extraordinarily high production values of the book. The notation for symmetry utilizes different colors in a way that is clear and helpful. The pictures are carefully done. Frankly, this is one of the most beautiful books I've ever owned.

My one complaint is that the corner of the cover of the copy I got from Amazon was a bit bent. It seems like too much trouble to ship it back and get a whole new copy for this, since the text is fine. This is quite unusual for Amazon, however.

In any case, I highly recommend this book for anyone interested in mathematics or even in art, from curious high school students to professional mathematicians.
15 von 18 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen good summary but tough going 15. April 2010
Von H. H. Leach - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
This book provides a very detailed overview of two and three dimensional symmetry types, but for the non-mathematician it can be tough going as the book progresses.
6 von 8 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen All symmetries, most beautiful 1. Juni 2013
Von Anne van Rossum - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Von Amazon bestätigter Kauf
This is not an ordinary book. It is really beautiful, really beautiful! And on the other hand it isn't afraid of describing the actual mathematical concepts. This is not an ordinary book, it really shows you have things can be visualized, from depicting how to "zip" the almost ghost-like blobs in Fig.8.2-5, that the order of operators in a group matters with a simple sketch in chapter 9, up to so many different views on the problems, that it would do no justice to the book to just have an enumeration here.

This is the type of book I wish my parents had in their library when I was 16. Yes, it has many concepts that you will not be taught at high school, however, the visualisations and the patient tour from the authors, makes this a perfect book for an autodidact. You can do the rotations and mirroring of the beautiful Escher-like patterns in your head and are constantly taken one step further in the book to understand the underlying regularities. I feel this book is much more comparable to learning how to tie complex knots, then to learn, say, linear algebra.

The only thing that would have benefited the reader, would be the connection to other scientific disciplines. It would be great to see so now and then what group theory brought to the table in chemistry, physics, cryptography, or machine learning. Especially, because the authors are not afraid to present complex mathematical objects, it might be trivial for them to do this and tell stories that are really hard to tell without such a detailed exposition as in this book.

For me this book is like "Gödel, Escher, Bach" to me.
0 von 1 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Has nice pictures 25. Januar 2014
Von Roger Bagula - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
I suppose that Bathsheba Grossman sculptures are the best way to illustrate the
actual faults of the book: the group descriptions of these works of art aren't really
enough mathematically to turn the pictures into usable mathematics.
The good thing about the book is the presentation of some very good tilings
in two and three space: the bad thing is that turning those groups into actual
graphics is 2d and 3d is not really a part of the book?
I find the book useful, but maybe not living up to the hype....
14 von 38 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Cristal 16. Dezember 2008
Von Mihai Prunescu - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
Very clearly explained and genially illustrated. One has the feeling that one understands the first time in ones life the topics presented -- e. g. the cristalographic groups.
Waren diese Rezensionen hilfreich?   Wir wollen von Ihnen hören.
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