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As a companion to mathematical Cranks, the MAA is happy to offer its readers another Dudley classic., The Trisectors. This book is also about mathematical cranks-angle trisectors.

It is impossible to trisect angles with straightedge and compass alone, but many try and think they have succeeded. This book is about angle trisections and the people who atempt them. Its purposes are to collect many trisections in one place, inform about trisectors, amuse the reader, and perhaps most importantly, reduce the number of trisectors. This book includes detailed information about the perssonalities of trisectors and their constructions.

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 at the end of the sections, 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." ... Read more

Customer Reviews (1)

Extreme examples of mathematical stubborness and illiteracy
...
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 ... Read more

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Each of the diagrams in this book poses a geometrical puzzle which has to solved simply by looking, thinking and imagining. For instance, what would you see if you look further into that hollow cube? By making models or using the cut-outs in the back of the book it is possible to check answers. ... Read more

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Formatted for Kindle. Linked Contents & Index. Illustrated.

From Preface:
On the question of Mathematical Puzzles in general there is, perhaps, little more to be said than I have written elsewhere. The history of the subject entails nothing short of the actual story of the beginnings and development of exact thinking in man. The historian must start from the time when man first succeeded in counting his ten fingers and in dividing an apple into two approximately equal parts. Every puzzle that is worthy of consideration can be referred to mathematics and logic. Every man, woman, and child who tries to "reason out" the answer to the simplest puzzle is working, though not of necessity consciously, on mathematical lines. Even those puzzles that we have no way of attacking except by haphazard attempts can be brought under a method of what has been called "glorified trial" — a system of shortening our labours by avoiding or eliminating what our reason tells us is useless. It is, in fact, not easy to say sometimes where the "empirical" begins and where it ends.

When a man says, "I have never solved a puzzle in my life," it is difficult to know exactly what he means, for every intelligent individual is doing it every day. The unfortunate inmates of our lunatic asylums are sent there expressly because they cannot solve puzzles — because they have lost their powers of reason. If there were no puzzles to solve, there would be no questions to ask; and if there were no questions to be asked, what a world it would be! We should all be equally omniscient, and conversation would be useless and idle.

It is possible that some few exceedingly sober-minded mathematicians, who are impatient of any terminology in their favourite science but the academic, and who object to the elusive x and y appearing under any other names, will have wished that various problems had been presented in a less popular dress and introduced with a less flippant phraseology. I can only refer them to the first word of my title and remind them that we are primarily out to be amused — not, it is true, without some hope of picking up morsels of knowledge by the way. If the manner is light, I can only say, in the words of Touchstone, that it is "an ill-favoured thing, sir, but my own; a poor humour of mine, sir."

As for the question of difficulty, some of the puzzles, especially in the Arithmetical and Algebraical category, are quite easy. Yet some of those examples that look the simplest should not be passed over without a little consideration, for now and again it will be found that there is some more or less subtle pitfall or trap into which the reader may be apt to fall. It is good exercise to cultivate the habit of being very wary over the exact wording of a puzzle. It teaches exactitude and caution. But some of the problems are very hard nuts indeed, and not unworthy of the attention of the advanced mathematician. Readers will doubtless select according to their individual tastes.

In many cases only the mere answers are given. This leaves the beginner something to do on his own behalf in working out the method of solution, and saves space that would be wasted from the point of view of the advanced student. On the other hand, in particular cases where it seemed likely to interest, I have given rather extensive solutions and treated problems in a general manner. It will often be found that the notes on one problem will serve to elucidate a good many others in the book; so that the reader's difficulties will sometimes be found cleared up as he advances. Where it is possible to say a thing in a manner that may be "understanded of the people" generally, I prefer to use this simple phraseology, and so engage the attention and interest of a larger public. The mathematician will in such cases have no difficulty in expressing the matter under consideration in terms of his familiar symbols. ... Read more

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How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers. ... Read more

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One of a series of sticker books, this title introduces the concept of sorting. It contains activities based on a household theme and features familiar objects to sort by size, shape and colour. The stickers can be used to solve puzzles including mazes, spot-the-difference and dot-to-dot puzzles. ... Read more

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Unique hands-on learning!

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Can you cut an octagon into five pieces and rearrange them into a square?How about turning a star into a pentagon? These are just two of the infinite challenges of geometric dissections, the mathematical art of cutting figures into pieces that can be rearranged to form other figures, using as few pieces as possible. Through the ages, geometric dissections have fascinated puzzle fans and great mathematicians alike. Here are dissections known to Plato and exciting new discoveries alike. Greg Frederickson explains solution methods carefully, assuming only a basic knowledge of high school geometry. This beautifully illustrated book provides hours of enjoyment for every mathematical puzzle enthusiast. ... Read more

Customer Reviews (1)

Slicing and splicing for enjoyment
Dissections are one area of mathematics where theory usually plays a secondary role to intuition.While the discovery of a solution may take an enormous amount of trial and effort, understanding it is generally a simpleverification. For these reasons, dissections can aptly be described as anarea of popular mathematics. The puzzles of Sam Loyd were extremelypopular, with one even described as having been a national craze in theUnited States, and some of his most diabolical were dissections. HisEnglish counterpart and rival was Henry Dudeney, whose collected works ofpuzzles also contains many dissections.
As befits the development ofabstract geometry centuries ago, the art of dissection goes all the wayback to the age of Plato. Starting with a geometric shape and cutting itinto pieces that can be rearranged to form another shape is something thatclearly is more of a hobby than a career, although it is possible that itmay have some applications in space filling.
Art and hobbies aside,this is a fun book to explore. Since the subject matter is the slicing andsplicing of geometric figures, most of the results are presented asdiagrams, making the solutions easy to understand. One thought constantlyleapt to mind when I was examining some of the diagrams,"How did theythink of doing that?" Obvious only after the fact, many dissections arehardly something that would easily leap to mind.Additional puzzles areinterspersed throughout the text and solutions to all are included at theend of the book.
The public loves puzzles, as the popularity of somegame shows and regular puzzle columns in newspapers and magazinesdemonstrates. In this book, you will find some of the most challenging ofdissection type puzzles, sure to keep you interested from the opening sliceto the final splice.

Published in Journal of RecreationalMathematics, reprinted with permission. ... Read more

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If you enjoy beautiful geometry and relish the challenge and excitement of something new, the mathematical art of hinged dissections is for you. Using this book, you can explore ways to create hinged collections of pieces that swing together to form a figure.Swing them another way and then, like magic, they form another figure! The profuse illustrations and lively text will show you how to find a wealth of hinged dissections for all kinds of polygons, stars and crosses, curved and even three-dimensional figures. The author includes careful explanation of ingenious new techniques, as well as puzzles and solutions for readers of all mathematical levels. These novel and original dissections will be a gold mine for math puzzle enthusiasts, for math educators in search of enrichment topics, and for anyone who loves to see beautiful objects in motion. ... Read more