The Trisectors (Spectrum) [Paperback]

Underwood Dudley (Author)

Book Description

Publication Date: September 1996 | ISBN-10: 0883855143 | ISBN-13: 978-0883855140 | Edition: 2nd

Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another - angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. According to Dudley: 'Hardly any mathematical training is necessary to read this book. There is a little trigonometry here and there, but it may be safely skipped. There are hardly any equations. There are no exercises and there will be no final examination. The worst victim of mathematics anxiety can read this book with profit and dry palms. It is quite suitable to give as a present.'

Editorial Reviews

Review

' ... it is a fascinating book, written in a most readable style seasoned with a sense of humor which caused me frequently to chuckle.' The Mathematical Gazette

Book Description

Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another - angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them.

See all Editorial Reviews

Product Details

• Paperback: 202 pages
• Publisher: The Mathematical Association of America; 2nd edition (September 1996)
• Language: English
• ISBN-10: 0883855143
• ISBN-13: 978-0883855140
• Product Dimensions: 9.2 x 6 x 0.4 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,298,798 in Books (See Top 100 in Books)

More About the Author

Underwood Dudley was born in New York City quite a number of years ago. He got bachelor's and master's degrees (mathematics) at what was then the Carnegie Institute of Technology. After working for a time for the Metropolitan Life Insurance Company, he gave up his promising future as an actuary to flee back to academia, attaining the Ph.D. degree (number theory) at the University of Michigan in 1965. After two years at the Ohio State University and thirty-seven at DePauw University (Greencastle, Indiana) he lay down his chalk and eraser and retired to Tallahassee, Florida, never again to grade a calculus test.

He has done quite a bit of editing in his time--the College Mathematics Journal for five years, the Pi Mu Epsilon Journal for three, the Dolciani Mathematical Expositions book series (six years), and the New Mathematical Library book series (three years). As a result he has a complete grasp of the distinction between "that" and "which" (very rare) and the conviction that no writing, including this, should appear before the public before passing through the hands, eyes, and brain of an editor. Take that, bloggers!

He believes that there is no greater achievement of the human intellect than mathematics, and that the study of mathematics provides great benefits, even to people who think that they hate it.

None of his four children or six grandchildren has entered the family business, but that's the way it goes.

Customer Reviews

Most Helpful Customer Reviews

4.0 out of 5 stars A must read for all trisectors!, February 17, 2012

By 

JO SEVENFIVETHREE "JO 753" (IL) - See all my reviews
(REAL NAME)   

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This review is from: The Trisectors (Spectrum) (Paperback)

Dr. Underwood Dudley seems to have a love/hate relation to trisectors; he has pursued the subject for decades, even visiting some of the people, avidly collects trisection attempts, yet constantly derides them and vehemently discourages anybody from trying to trisect an angle. His picture on the back of the book is perfect. He appears to be restraining a curled lip of disgust as he speaks with a typical trisector.

He classifies trisecting as a disease, so maybe his obsession is a mutated form of it? This is how the virus manifests in a Ph.D. mathematician.

I believe at least part of the motivation for writing the book is Dudley's admiration for Augustus De Morgan, a mathematician of the 1800's who wrote a book about cranks attempting the 3 popular impossibles. Dudley frequently quotes him and named the major section of The Trisectors A Budget of Trisections emulating De Morgan's A Budget of Paradoxes.

As a trisector, I found the book very informative and entertaining. He goes to some lengths to describe and analyze each of the 103+ trisections he has collected from many sources, providing a sketch, construction sequence and resulting level of precision for most, plus a brief story about each of the creators.

A few complaints:

In the first chapters, he often inserts a quotation without warning, leaving one to wonder after a paragraph if it's his statement or another De Morgan quote. Thruout the book, quotes are indicated only by indentation and maybe the preceding sentence.

Much worse is the reduction of all the trisectors names to serialized or alphabetized by last name inititials. So each entry contains, for example, "C arranged point D by intersecting C with BC" leaving you to puzzle out if this is the guy's initial or a point in the diagram. Plus, since the surrounding entrys will also often have the same last initial and he will often refer to different trisections in the book, any interest in investigating the reference is discouraged by the layered confusion. I don't know if Dr. Dudley choose this approach or if the lawyers decided that it would help avoid lawsuits.

In spite of these complaints, It is an excellent book for anybody interested in the subject. The most revealing thing for me was the incredible variety of trisection attempts.

1 of 4 people found the following review helpful:

4.0 out of 5 stars Extreme examples of mathematical stubborness and illiteracy, March 27, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: The Trisectors (Spectrum) (Paperback)

...
Lively, entertaining, frustrating and sometimes a majordowner, this book should be read by all who wish to raise the tide ofmathematical literacy.

Published in Journal of Recreational Mathematics, reprinted with permission. END

0 of 3 people found the following review helpful:

4.0 out of 5 stars Why trisectors may have a point., September 12, 2011

By 

Siavash Sohrab "Thomas Jefferson" (USA) - See all my reviews
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Amazon Verified Purchase

This review is from: The Trisectors (Spectrum) (Paperback)

The book by Professor Underwood Dudley is very interesting and enjoyable to read. However, his criticism of all trisectors amongst both professional as well as amateur mathematician since the important 1837 paper of Wantzel is too harsh. It could be argued that since Wantzel (1837) theory involves rational numbers it may not apply to the trisection problem because trisecting angles necessarily involves the important number 3.1415... and hence transcendental numbers that are not roots of polynomials with constant coefficient.