Mathematics and Art [Hardcover]

Claude P. Bruter (Editor)

Book Description

ISBN-10: 3540434224 | ISBN-13: 978-3540434221 | Publication Date: October 3, 2002 | Edition: 1

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.

Editorial Reviews

Review

From the reviews: "This book gives a summary of a Colloquium held in Maubeuge (France) in September 2000. The Colloquium was based on the relations between Arts and Mathematics (in particular, on the art of visualization of mathematics), and contained a collection of 27 talks given by artists as well as mathematicians … . An Appendix of more than fifty pages at the end of the book shows beautiful pictures of models, sculptures and computer graphics linked to the papers discussed. A beautiful book!" (I. Pola, Nieuw Archief voor Wiskunde, Vol. 5/4 (4), 2003) "This book contains the proceedings of a Colloquium on Mathematics and Art held in Maubeuge (France) in September 2000. … The References give a comprehensive list of sources for further study and most papers refer to websites which widen the reader’s appreciation of the topic. … Readers … will find some of the themes and related material developed in the book of interest. Some readers will find considerable value in having the book as a reference." (W. P. Galvin, The Australian Mathematical Society Gazette, Vol. 30 (2), 2003) "This book must have been a delight to put together. It contains 28 essays by 25 authors from 8 countries, and covers at least 5 disciplines (mathematics and art, of course, but also computer science, film and music). … The strength of this collection of works is that it comes from a collection of talented people who have a lot to say on the subject of visualization in mathematics and art." (Annalisa Crannel, MAA Online, April, 2003)

From the Back Cover

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. This book emphasizes and renews the deep relation between Mathematics and Art. The Forum Discussion suggests to develop a deeper interpenetration between these two cultural fields, notably in the teaching of both Mathematics and Art.

Product Details

• Hardcover: 497 pages
• Publisher: Springer; 1 edition (October 3, 2002)
• Language: English
• ISBN-10: 3540434224
• ISBN-13: 978-3540434221
• Product Dimensions: 9.3 x 6.3 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,823,717 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

3 of 3 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

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calvinnme - See all my reviews
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This review is from: Mathematics and Art (Hardcover)

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.

4.0 out of 5 stars Not for the faint of heart, December 17, 2010

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Frederico Lopes (Brazil) - See all my reviews
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This review is from: Mathematics and Art (Hardcover)

Good book. Not only visual, but also aural: there are several articles on mathematics of music. Very good ideas for mathematical artists, but in a little strict terms. Speaking seriously, the images are creations of mathematicians, not artists...