The Manifold Beauty of Piano-hinged Dissections
Greg N. Frederickson: The Manifold Beauty of Piano-hinged Dissections. In: Bridges 2005. Pages 1–8
A geometric dissection is a cutting of one geometric figure into pieces that we can rearrange to form another. For some dissections, it is possible to hinge the pieces together, so that we can flip the pieces one way on the hinges to form one figure, and flip them another way to form the other figure. When the hinge connects two pieces along a shared edge in both target figures, the movement corresponds to a folding. We call such dissections piano-hinged dissections. This paper explores design methods and properties of piano-hinged dissections.
 Henry E. Dudeney. Puzzles and prizes. Column in Weekly Dispatch, 1896–1903.
 Henry Ernest Dudeney. The Canterbury Puzzles and Other Curious Problems. W. Heinemann, London, 1907.
 Henry Ernest Dudeney. Puzzles and Curious Problems. Thomas Nelson and Sons, London, 1931.
 William L. Esser, III. Jewelry and the like adapted to define a plurality of objects or shapes. U.S. Patent 4,542,631, 1985. Filed 1983.
 Greg N. Frederickson. Dissections Plane & Fancy. Cambridge University Press, New York, 1997.
 Greg N. Frederickson. Hinged Dissections: Swinging and Twisting. Cambridge University Press, New York, 2002.
 Greg N. Frederickson. Piano-hinged dissections: now let’s fold. In Jin Akiyama and Mikio Kano, editors, Discrete and Computational Geometry, Japanese Conference, JCDCG 2002 Revised Papers, volume LNCS 2866, pages 159–171. Springer, 2003.
 Greg N. Frederickson. “Piano-Hinged Dissections: Time to Fold”. Completed draft of a manuscript, 320 pages, 2004.
 Greg N. Frederickson. Hinged dissections: Swingers, twisters, flappers. In M.L. Demaine B. Cipra, E.D. Demaine and T. Rodgers, editors, A Tribute to a Mathemagician, pages 185–195. A K Peters, Ltd., Wellesley, Massachusetts, 2005.
 Solomon W. Golomb. Polyominoes : Puzzles, Patterns, Problems, and Packings. Princeton University Press, Princeton, 2nd edition, 1994.
 Harry Lindgren. Geometric Dissections. D. Van Nostrand Company, Princeton, New Jersey, 1964.
 Sam Loyd. Mental Gymnastics. Puzzle column in Sunday edition of Philadelphia Inquirer, 1898–1901.
 Geoffrey Mott-Smith. Mathematical Puzzles for Beginners and Enthusiasts. Blakiston Co., Philadelphia, 1946. Reprinted by Dover Publications, New York, 1954.