The Symmetries of Things 1st Edition by John H. Conway (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐This is the first review of a book I’ve ever posted on Amazon. I just want to say that if you’re a non-mathematician this book may still have something to interest and intrigue you. I have taught it to math phobic non-math majors at the collegiate level, and it went over pretty well. If you’re thinking it looks interesting but “too mathy” maybe you should take the plunge. There’s plenty of math in there, but it’s presented very gently. Or at least gently enough that a classroom full of people who have tried to avoid math all their lives found non-intimidating.

⭐I love the progressive difficulty of the book. The first view chapters are accessible to anyone and a great tool for getting and understanding of symmetries in the world around you.

⭐The Symmetry of Things is a fantastic resource for mathematicians and artists alike. The artwork inside is amazing! And the book has spawned a great deal of artwork inside the mathematical art community. I thank the authors for this tremendous contribution to the literature.

⭐This book has extremely high production values – the graphics are magnificent. It is interesting to see the kind of topics that occupy mathematicians who study symmetry intensely.

⭐This came fast and in good shape. What a good reference and study book!

⭐One of my new favorite books!

⭐This is a great book. I had some misgivings at first: I did not like some of the terminology and I found some of the language a little vague. However, having penetrated much further into its depths, I find it quite awe-inspiring. Its presentation is second to none; it is jam-packed with beautiful illustrations. Although it is very mathematical, there is plenty to delight the non-mathematical reader. I have not seen another maths book that treats symmetry in as much depth or does it so well as this – or even comes close. A marvellous achievement. I think it deserves two more stars, so here they are: * *.

⭐I bought this book for my son for Christmas as he had requested it. He had already seen a copy and is very pleased with the content and the high quality of the content and the publication.It’s fine if you like maths etc.!

⭐Halfway through the book and finding the classification system quite interesting. Lots of good illustrations in the book as well.

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