Customer Reviews

Piano-hinged Dissections: Time to Fold!

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While the dissection of a geometric object is generally easy to follow after the fact, the dissections in this book at times are very difficult to understand. A piano hinge dissection is one where a hinge runs the full length of a joint. The analogy is to the hinge that allows the top of a grand piano to be opened although in this case the hinge can allow the two pieces to be folded in either of the two directions. Add in multiple hinges and the potential for the pieces to overlap and the additional degrees of freedom can make for a complicated structure. I often found myself wondering how the dissection had been discovered.
While Frederickson uses very detailed and multiple diagrams with different styles of hashing of the lines to describe the dissections in the book, they are often hard to follow. That is not meant to be a criticism; much of the difficulty is due to the complexity and originality of the dissections. A good deal of this is solved by the videos on the CD that accompanies the book. In them, Frederickson uses paper and wooden models to illustrate the folding that allows you to transform one figure into another. Seeing the transformation by executing one active fold after another makes it so much clearer. Quite honestly, I am not sure if I would have completely grasped some of the more complex transformations without the video.
The use of one or more piano hinges in a dissection creates a significantly higher level of complexity. However, in complexity there is joy and while I had difficulty in the explanations, the wonder of seeing it work made the time of difficulty well spent.

Published in Journal of Recreational Mathematics, reprinted with permission.