The Golden Section (Spectrum) [Paperback]

Hans Walser (Author), Jean Pedersen (Translator), Peter Hilton (Translator)

Book Description

ISBN-10: 0883855348 | ISBN-13: 978-0883855348 | Publication Date: July 15, 2001

The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. In this way, the Golden Section is no isolated phenomenon but rather, in many cases. the first and also the simplest non-trivial example in the context of generalisations leading to further developments. It is the purpose of this book, on the one hand, to describe examples of the Golden Section, and on the other, to show some paths to further extensions. The treatment is informal and the text is enriched by the presence of very illuminating diagrams. Questions are posed at fairly frequent intervals and the answers to these questions, perhaps only in the form of very broad hints for their solution, are gathered together at the end of the text.

Editorial Reviews

Book Description

The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. This book aims both to describe examples of the Golden Section, and to show some paths to further developments.

About the Author

Hans, Walser is a teacher at the State College of Thurgau in Switzerland and lecturer at the ETH Zürich (Swiss Federal Institute of Technology) and the University of Basel. He received his Ph.D from the ETH Zürich in 1975. His primary research interest is in geometry. He is currently involved in the instruction and education of future high school teachers. He was a visiting guest and lecturer at Santa Clara University in 1996 and 1998. The Mathematical Association of America has also published the English translation of "Symmetry," by Hans Walser.

Product Details

• Paperback: 133 pages
• Publisher: The Mathematical Association of America (July 15, 2001)
• Language: English
• ISBN-10: 0883855348
• ISBN-13: 978-0883855348
• Product Dimensions: 8.8 x 5.9 x 0.4 inches
• Shipping Weight: 7.2 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,653,900 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 17 people found the following review helpful:

5.0 out of 5 stars A TOPIC TO TIE IN SEVERAL MATHEMATICAL SUBJECTS, March 6, 2002

By 

JON STRICKLAND "Jon Strickland" (Smithfield, NC United States) - See all my reviews
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This review is from: The Golden Section (Spectrum) (Paperback)

The Golden Section is a very fascinating topic that is applied in several fields, both mathematical and nonmathematical. Why? Because this number primarily focuses on proportion, both in a physical and numerical context.

Somewhat to my chagrin, the author confines this subject within the realm of mathematics. For I wish that the Golden Section was discussed from a thematic or historical standpoint, such as how or why artists such as Da Vinci used this concept in order to construct or create works of art that were well-proportioned.

Nonetheless, the mathematics is delightfully presented. It is sketchy in some areas but is much easier to follow than several of the 50+-year-old-mathematical works that have not been revised or updated. Fascinatingly, this one topic alone synthesizes or ties in several mathematical disciplines, including: fractals, geometry, topology, number theory, trigonometry, and, strangely enough, probability.

I highly recommend this book. It is neat and concise, and it is a great reference for the mathematician who has been out of practice for a while to brush up on his or her skills.

5.0 out of 5 stars A book for mathematicians at all levels, December 24, 2011

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: The Golden Section (Spectrum) (Paperback)

This short book of examples of where the golden section appears in geometry requires no mathematical background beyond that of basic algebra and trigonometry. It is not a book of examples where the golden ratio appears in nature, the demonstration is of geometric structures such as fractals, solids, paper folding and number sequences. Problems for further exploration are interspersed within the exposition and brief solutions are included at the end.
This is a book that all mathematicians can read and enjoy, from the advanced high school student up through the professional. All teachers from late middle school through college can find example problems to challenge their students. Even late elementary school students can be directed through some of the iterated processes of cutting and folding.