Mathematics and Art (Hardcover)

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Product Description

Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.

Product Details

• Hardcover: 497 pages
• Publisher: Springer; 1 edition (October 3, 2002)
• Language: English
• ISBN-10: 3540434224
• ISBN-13: 978-3540434221
• Product Dimensions: 8.7 x 5.6 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,948,634 in Books (See Bestsellers in Books)

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1 of 1 people found the following review helpful:

3.0 out of 5 stars There are some gems but you'll need to dig to find them, July 13, 2007

By	calvinnme "Texan refugee" (Fredericksburg, Va) - See all my reviews (TOP 10 REVIEWER)

The authors of this compilation of articles are quite varied and include both artists and mathematicians who each have an article in this little book. Each of them has a lot to say on the subject of visualizing mathematics and the place of mathematics in art, unfortunately each of them seems to be talking to a different audience. This is the typical trouble you frequently encounter with a book that is a series of articles by a number of authors versus one consolidated textbook. Several of the articles that are centered on math completely avoid formulas while others carefully define all terms and go very deep into theoretical mathematics. To make matters somewhat more confusing, the articles are not in order of topic. Finally, several articles contain large amounts of philosophical or historical reflections on projects that are obviously important to the author, yet the author never bothers to introduce said project to the uninitiated reader. It is as though these particular articles were written by insiders for insiders.

However, there are some little gems in this book. There is a very good article by George Hart that includes an algorithmic description of how to build polyhedral sculptures in both computer and physical terms. This article should be read by anyone interested in platonic solids, and it includes much practical advice. I also really liked three of the articles on the relationship between math and music. Neuwirth has an article that describes the mathematical history of instrument tuning in which he includes Mathematica code that enables the reader to experiment with the procedure and hear the results. Simoes' article describes the algebra behind Schoenberg's 12-tone construction. Hellegouarch's article is a good follow-on to Simoes' offering in that he offers the algebra of how singers can break the algebraic rules behind our usual mathematical scale and get away with it. There are two very good articles linking dynamical systems to the aesthetics of pleasing visual design. Finally, there are a couple of articles on how to integrate mathematics and art into a course. One of the authors describes a course he taught on knots that led to an exhibition. Another explains how he used his own computer program as the centerpiece of an interdisciplinary course for art students.

In conclusion, this book is very uneven as are many books that consist of articles by different authors, but it does have some unique and worthwhile entries that do fall under the banner of connecting math to art. You'll just need to wade through several overly theoretical papers that don't seem to go anywhere as far as the math/art connection go.