Symmetry

by Hermann Weyl

Book Overview

Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract...

• Format: Paperback
• Language: English
• ISBN: 0691023743
• ISBN13: 9780691023748
• Release Date: January 1983
• Publisher: Princeton University Press
• Length: 176 Pages
• Weight: 0.53 lbs.
• Dimensions: 0.5" x 5.5" x 8.5"

Customer Reviews

Overall summetry

Very well written introductory book to symmetry-group theory notions concise and thought provoking lacking some modern notions and strong mathematical deductions Can be read from high scool students an easy pace book ideal for a first contact with the subject

a difficult but rewarding introduction to mathematical symmetry and some of it's applications

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.

An excellent introduction to the concept of symmetry

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.

Symmetry Package

This book came promptly, in perfect condition. Much more affordable than through the college bookstores.

Ornamentation and its mathematical basis

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).