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Prof. Frederickson: Time to Fold


Piano-Hinged Dissections book cover

Prof. Greg Frederickson's third book Piano-Hinged Dissections: Time to Fold! was recently released by A.K. Peters. In this book Prof. Frederickson introduces the surprising new concept of piano-hinged geometric dissection. The book is an outline of methods for creating this type of handiwork and it describes over 150 challenges in folding, using line drawings and 3D perspectives. Prof. Frederickson says piano-hinged dissections, "are challenging to discover and difficult to illustrate. Yet, paradoxically, you need relatively little background to understand and enjoy them," making this a book for anyone with experience in high school geometry.

Piano-hinged dissections differ from standard dissections in that standard dissections cut a geometric shape into a number of pieces that can be rearranged to form a second shape. In a piano-hinged dissection, the pieces are attached together so that you can use a folding motion to move the pieces from one shape to the other. The term "piano-hinged" comes from the long, narrow hinge that connects the lid of a grand piano to its sound box. A fun example from the book is in figure 4.5 (click the diagram pictured for a larger version) which transforms an ellipse into a heart with just a few folds. This folding motion is reminiscent of what you see in origami, the Japanese art of paper-folding.

Piano-Hinged Dissections: Time to Fold! includes a compact disc that provides 50 demonstrations of Prof. Frederickson's work. In this one-man show Prof. Frederickson played the hand actor, director, scriptwriter, producer, cinematographer, cameraman, art director, editor and narrator. Although he had fun doing so, he included the CD to encourage readers to try the examples provided in the book. Some of the models shown on the CD are made out of wood, but as an added effort to get readers involved the remainder are made out of thick colored paper. Since he shows no special materials are needed, everyone can try their hand at these clever puzzles. Piano-Hinged Dissections: Time to Fold! is available from the publisher, from and other internet booksellers. It is also available in stores such as Barnes and Noble Books and Borders, either on the shelf or by order.

Prof. Greg Frederickson has been a professor at Purdue University Department of Computer Science since 1982. His areas of interest include the analysis of algorithms, with special emphasis on data structures, and graph and network algorithms. Prior to Piano-Hinged Dissections: Time to Fold!, he published Dissections Plane & Fancy in 1997 and Hinged Dissections: Swinging & Twisting in 2002 both with Cambridge University Press.

Transforming an ellipse into a heart

Last Updated: Jun 29, 2023 12:00 PM

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