A Special Afterword
First let me thank Tom Rodgers for having started the Gardner Gatherings and nurturing them into a unique meeting of persons interested in recreational mathematics, mechanical puzzles, and conjuring. I recently received a letter from the well-known IBM mathematician and writer Clifford Pickover telling me how much he enjoyed his first visit to the (eighth) gathering.
And of course I am equally honored and grateful to Ray Hyman for his account of this year’s gathering. I wish I could have been there and renewed acquaintances with so many good friends in the worlds of mathematics and magic. Ray mentions that several mathematicians gave proofs of unusual theorems. Allow me to cite one—an unexpected proof that was of special interest to me.
In one of my early Scientific American columns I reported on the famous discovery by England’s great puzzle maker Henry E. Dudeney of a way to slice a square into as few as four pieces such that if made of wood they could be hinged to form a chain that could be unfolded then folded a different way to make an equilateral triangle! Greg Frederickson, a mathematician at Purdue, is the world’s top expert on geometric dissections. His latest book, Plano Hinged Dissections: Time to Fold! (A.K. Peters 2006), deals entirely with his discoveries of beautiful hinged dissections.
At the last gathering, Erik Demaine, a young computer scientist at MIT, explained his remarkable proof, yet to be published, that any polygon of any shape can be cut into a finite number of pieces that can be hinged to form a chain that will fold to make any other given polygon of the same area! It is a great breakthrough in hinged dissection theory. Of course the task, far from easy, is to find a way to make the chain with a minimum number of pieces. I’m told that Demaine’s presentation produced prolonged applause.
Thanks, Ray, for bringing back so many happy memories.