Plane & Fancy

Greg N. Frederickson


As befits a book on recreational mathematics, this one has been great fun to write, in part because I let my curiosity lead the way. It was a revelation to survey the original puzzle columns of Dudeney in The Strand Magazine of the 1910s and 1920s. It was fascinating to dig out even earlier references and make connections that other authors had missed. It was intriguing to collect biographical information on the people who have made a contribution to this area.

I hope that the book will also be great fun to read. The intended audience is anyone who has had a course in high school geometry and thought that regular hexagons were rather pretty. I have used some other high school math here and there. If you find some of the formulas tough sledding, you should be able to skip over them without much lost. Likewise, if you skip over the algorithmlike Descriptions of methods in Chapters 7-9, you won't lose much but can be comforted that precise Descriptions do exist. On the other hand, if you get intrigued with some topic and want to follow up on it, I have provided additional comments and references, ordered by chapter, in the Afterword.

It has been a surprise to see how many people have contributed to whatever success this book may enjoy. First are those who have produced new dissections, in quality and quantity substantially greater than I had imagined. I gratefully acknowledge the permission of Diulio Carpitella, Anton Hanegraaf, Bernard Lemaire, David Paterson, Robert Reid, Gavin Theobald, and Alfred Varsady to reproduce their unpublished or privately published dissections.

Martin Gardner is the unofficial godfather of this book. A letter from him got me thinking about dissections again in 1991. And when I started on the book in 1994, he was generous with his help and advice. Some of his leads were crucial. He forwarded a decade- old letter from Robert Reid that led to an especially fruitful interaction. And Martin also put me in touch with Will Shortz, and that contact led to a fortunate chain of events. Will generously provided me with the citations to the earlier versions of dissection puzzles that later appeared in Sam Loyd's Cyclopedia. And Will also told Jerry Slocum what I was up to. Jerry clued me in to the trade cards that Sam Loyd had produced, and he shared copies from his puzzle collection with me. Jerry also alerted me to David Singmaster's wonderful work on sources of recreational mathematics. David shared an electronic copy of his book, and xerox copies of Dudeney's puzzle columns in the Weekly Dispatch, too. David's sources book helped me focus on earlier historical material. It also led to my contact with Anton Hanegraaf, who generously shared his treasure trove of unpublished material with me. Anton also provided a scholarly critique of a draft of my first chapter on solid dissections, accompanied by an additional annotated bibliography.


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