A dissection involves cutting a polygon into pieces in such a way that those pieces form another polygon; for a hinged dissection, the pieces must be attached by hinges. A piano hinge is a long narrow hinge with a pin running the entire length of its joint. So, unlike regular hinged dissections, which swing or twist (around single point of hinge), piano-hinged dissections fold along an edge. This book discusses the history, methods, and variations of these dissections and is rich with illustrations that clearly depict the cuts of the dissections and three-dimensional simulations of the dissections in the process of being folded. A CD that includes video recordings of select dissections being transformed accompanies the book.
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Greg Frederickson s ability to discover (or should I say create?) elegant dissections, hinged, folded, or otherwise, is awesome. His beautiful book contains challenges that will keep recreational geometricians happily at work for decades. A bibliography runs to more than 120 references! --Martin Gardner
About the Author
Greg N. Frederickson is a professor of computer science at Purdue University. He has written two previous books on dissections Dissections: Plane & Fancy (1997) and Hinged Dissections: Swinging & Twisting (2002), and is considered an international authority on folding unusual polygonal geometries. He also won the 2004 Polya Award of the Mathematical Association of America for a related article.
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5.0 out of 5 stars
Complex, yet fascinating dissections with a flip,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Piano-hinged Dissections: Time to Fold! (Hardcover)
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.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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unhingeable dissection, swing hinged dissection, unhinged dissection, cyclic hinging, small hexagrams, two attached squares, cyclicly hinged, hinged dissections, large hexagram, twist hinge, dissection puzzles, square twist, piece dissection, previous dissection, swing hinges, hinged pieces, small hexagons, large hexagon, piano hinge, projected view, isosceles right triangles, dashed edges Key Phrases - Capitalized Phrases (CAPs): (learn more)
Piano-Hinged Dissections, Greek Cross, Ernest Freese, Harry Lindgren, Latin Crosses, Triangle Again, Robert Reid, Puzzles Unfolded, Pot Luck, Henry Dudeney, Manifold Blessings, Sam Loyd, What's the Flap, Los Angeles, Cross of Lorraine, Square Tactics, New Wrinkle, Ernest Irving Freese, Mixed Bag, Gavin Theobald, Alfred Varsady, David Paterson, Kay Dundas, Quad Squad Figure, Hanumanta Rau New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
unhingeable dissection, swing hinged dissection, unhinged dissection, cyclic hinging, small hexagrams, two attached squares, cyclicly hinged, hinged dissections, large hexagram, twist hinge, dissection puzzles, square twist, piece dissection, previous dissection, swing hinges, hinged pieces, small hexagons, large hexagon, piano hinge, projected view, isosceles right triangles, dashed edges Key Phrases - Capitalized Phrases (CAPs): (learn more)
Piano-Hinged Dissections, Greek Cross, Ernest Freese, Harry Lindgren, Latin Crosses, Triangle Again, Robert Reid, Puzzles Unfolded, Pot Luck, Henry Dudeney, Manifold Blessings, Sam Loyd, What's the Flap, Los Angeles, Cross of Lorraine, Square Tactics, New Wrinkle, Ernest Irving Freese, Mixed Bag, Gavin Theobald, Alfred Varsady, David Paterson, Kay Dundas, Quad Squad Figure, Hanumanta Rau New!
Books on Related Topics Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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