Symmetry

Rating:
Summary: Great Examination of Symmetry from a Mathematical Viewpoint
Review: 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.

Rating:
Summary: Ornamentation and its mathematical basis
Review: 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).