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Symmetry Paperback – January 21, 1983

ISBN-13: 978-0691023748 ISBN-10: 0691023743

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Product Details

  • Series: Princeton Science Library
  • Paperback: 176 pages
  • Publisher: Princeton University Press (January 21, 1983)
  • Language: English
  • ISBN-10: 0691023743
  • ISBN-13: 978-0691023748
  • Product Dimensions: 5.5 x 0.4 x 8.5 inches
  • Shipping Weight: 7.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #73,739 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Dr. Weyl presents a masterful and fascinating survey of the applications of the principle of symmetry in sculpture, painting, architecture, ornament, and design; its manifestations in organic and inorganic nature; and its philosophical and mathematical significance."--Scientific American



"Weyl offers deep insight into [the concept of symmetry], its foundations in group theory, its applications in physics, chemistry, and biology, and its role in art."--Manfred Eigen and Ruthild Winkler in Laws of the Game

Customer Reviews

4.8 out of 5 stars
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Good intro book.
Bruce Altimar
Unfortunately in the version I have the citations that Weyl makes are not clearly listed, but many of the authors are fairly prominent and easy to look up.
William M. Rand
Group theory is the mathematical language of symmetry, and the first chapter of this book discusses bilateral symmetry in depth.
Jason Dowd

Most Helpful Customer Reviews

62 of 62 people found the following review helpful By henrique fleming on July 22, 1998
Format: Paperback
This delightful booklet motivates the study of symmetry by showing its presence in art and nature. This is a work of love, frequently bordering poetry. Yet, it is a scientific book of high class. Hermann Weyl, one of the very great mathematicians of this century, then explains the mathematics behind symmetry, mostly group theory, and obtains all forms that, by repetition, completely fill the plane and the space (the crystallographic groups). This is wonderful reading. After it, the reader should be prepared for a beautiful recent discovery by R. Penrose, that there are aperiodical forms that completely fill the space, and, still more surprising, that Nature makes use of them. They are the quasi-crystals (not treated in Weyl's book, of course).
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37 of 39 people found the following review helpful By William M. Rand on July 6, 2000
Format: Paperback
Be forewarned this book is technical and mathematical. Though you can definitely read it without going through all the math and thinking it through it won't be nearly as valuable to you as it would be if you spent some time and actually thought things out and figured them out rather than just speeding through. That being said this is probably the best examination of symmetry out there that I have read. Weyl starts from very simple concepts and eventually works his way up to examining even complex ornamental symmetry. Of course much of what he says about symmetry is true of aesthetics and beauty in general and many parallels can be drawn between what he is saying and other items like music that may not appear to have clear symmetry right off the bat. Unfortunately in the version I have the citations that Weyl makes are not clearly listed, but many of the authors are fairly prominent and easy to look up. If you like this book I might also reccomend G. D. Birkhoff's Aesthetic Measures. Where, Weyl is interested more in just symmetry Birkhoff is interested in mathematical aesthetic examination in general. Overall this book is a must read for anyone interested in aesthetics.
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Format: Paperback
Symmetry is about the mathematical underpinnings of symmetry as it appears in nature and art. The book is divided into 4 sections, the first Bilateral Symmetry covers reflection. This lecture goes into biology and art. The next lecture is about rotational symmetry. I was able to follow the math presented in this lecture but had trouble in the 3rd lecture titled Ornamental Symmetry. Ornamental symmetry is mostly about tilings of the plane. There is a lot of math presented in this lecture. I had to fall back on my rudimentary knowledge or abstract algebra and linear algebra to understand it. My point is that without this knowledge this lecture and the next one The General Idea of Mathematical Symmetry would have been impossible for me to follow. However, I still recommend this book to people who don't have any of the above background. Symmetry covers the concepts behind symmetry well, and it's applications to nature and art can be followed by anyone.
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Format: Paperback
Symmetry is a fundamental characteristic of most living creatures, some natural features such as crystals, the basis of some mathematical models and a beautiful form of art. Most animals possess a form of bilateral symmetry, with only minor differences our right and left sides are mirror images of each other. Weyl gives examples of all of these types of symmetry, images with text explaining the details regarding the symmetry of the object.
At the end, he gives the mathematical explanations of the symmetries, how they can be combined into the construct known as a group. The symmetries can then be sequentially combined to perform multiple actions and generate other actions. This dual examination provides a great deal of insight into the idea of symmetry. Biologically, it is clear that there must be powerful evolutionary advantages to symmetry, as it is universal in the animal kingdom. Humans also have a natural affinity for symmetric objects, as symmetry is a universal theme in the art work of cultures with little or no contact between them.
Weyl has written an excellent introduction to the concept of symmetry. It is an idea that is easy to understand and the different motions of a symmetric object are a very good way to begin the study of group theory. Artists can also obtain some benefit from the additional knowledge of symmetry that they will get from this book.
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4 of 4 people found the following review helpful By Giant Panda on October 19, 2008
Format: Paperback
I thoroughly enjoyed reading this book. It offers very deep insights on the use and implications of symmetry, not only in art, but in physics, chemistry, and other sciences. It also provides a comprehensive mathematical treatment at an accessible level. The reason I did not give it a full 5 stars is that sometimes the mathematical steps were not fully spelled out, or the explanation was vague, so a few passages left me wondering what he really means. More examples, figures, and details would have helped. Still, it was an exciting read - for the first time I really understood the theory of relativity and what it means in terms of symmetry. The author also impresses with his breadth of knowledge, being equally comfortable with the latest mathematical methods as he is with historical development of the field, all the way back to the Egyptians and Greeks. The book is fairly slim and I read it fast, yet learned a lot.
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