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. Read more

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. Read more