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Hinged Dissections: Swinging & Twisting

Greg N. Frederickson
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Mihaela Poplicher
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Greg N. Frederickson, a Professor of Computer Science at Purdue University, has written two books on dissections, both published by Cambridge University Press: one in 1997, Dissections: Plane & Fancy, and, in 2002, Hinged Dissections: Swinging & Twisting. Both of them are intended, as the author writes in the preface of his second book, for those who "enjoy extraordinarily beautiful objects and relish the challenge of something new."

The book does not require more knowledge than high school geometry and is not a succession of theorems, followed by proofs, examples, applications and examples. Instead, the author includes detailed explanations of very ingenious new techniques, as well as puzzles (with solutions!) The book is a lot of fun to read, and the lively text includes hinged dissections for polygons (triangles, squares, stars, crosses, etc), as well as curved and three-dimensional figures. Since hinged dissections refer to the cutting of a geometric figure into hinged pieces that can be rearranged to form another figure, it is obvious that the book needed to include many illustrations. Of these, the author includes a wealth, and all of them are very good! Of course, it is even more fun to see some animations, and some of these can be found at

The above is just part of a much larger collection of new developments posted by the author at his web-page about the book. It is in this web-page that we find out about a paper by a McGill computer scientist and a few Harvard chemists describing animated dissections with chemical processes. The paper has been published in the Journal of the American Chemical Society, vol. 124, pp. 14508-14509.

This means that hinged dissections are not only fun and entertaining, but also useful outside mathematics — one more reason for everybody interested in finding entertaining and challenging mathematical puzzles, from high school students to mathematicians, to read Frederickson's book

Mihaela Poplicher is an assistant professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is [email protected].

1. If it ain’t got that swing; 2. Hinging on the details; 3. Tricks for turning; 4. Making squares dance; 5. L'affaire triangulaire; 6. Return to polygonia; 7. Who’s the squarest of them all?; 8. Stepping around; 9. All in the family; 10. Elation in tessellations; 11. Strips revealed; 12. With a little help from my friends; 13. At cross purposes; 14. Handling the curves; 15. And also starring; 16. Four of a kind; 17. As the whirled turns; 18. A new breed of swingers; 19. Not your regular polygons; 20. Into another dimension; 21. The flip side; 22. Twist and shout!; 23. Puzzles unhinged; Afterword; Bibliography; Index of dissections.