Hinged Dissections: Swinging and TwistingIf you enjoy beautiful geometry and relish the challenge and excitement of something new, the mathematical art of hinged dissections is for you. Using this book, you can explore ways to create hinged collections of pieces that swing together to form a figure. Swing them another way and then, like magic, they form another figure! The profuse illustrations and lively text will show you how to find a wealth of hinged dissections for all kinds of polygons, stars and crosses, curved and even three-dimensional figures. The author includes careful explanation of ingenious new techniques, as well as puzzles and solutions for readers of all mathematical levels. These novel and original dissections will be a gold mine for math puzzle enthusiasts, for math educators in search of enrichment topics, and for anyone who loves to see beautiful objects in motion. |
Contents
Hinging on the Details | 11 |
Making Squares Dance | 33 |
Return to Polygonia | 57 |
Stepping Around | 72 |
Elation in Tessellations | 93 |
With a little Help from my Friends | 119 |
At Cross Purposes | 126 |
And Also Starring | 139 |
Four of a Kind | 154 |
A New Breed of Swingers | 177 |
Not Your Regular Polygons | 192 |
The Flip Side | 210 |
Twist and Shout | 228 |
Puzzles Unhinged | 258 |
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Common terms and phrases
2-fold rotational symmetry 4-piece dissection 6-piece unhingeable dissection 7-piece 7-piece hingeable dissection angle Anton Hanegraaf convert Crossposing crossposition cube cyclicly hinged dashed edges decagon derive dissection in Figure dissection is hinge-snug dissection of five dissection of four dissection of squares dissection of three dodecagon dotted enneagon equal squares equilateral triangle flip hinge found a 7-piece give Greek Cross Harry Lindgren Henry Dudeney heptagons hexagon hexagram hinge-snug and grain-preserving hingeable dissection hinged assemblage hinged dissection hinged pieces isosceles right triangles isosceles triangles Latin Cross line segment mathematical Move/cut n-omino number of pieces octagon pair parallelogram pentagon pentagrams pieces in Figure puzzle Q-swing readers rectangle rhombuses rotational symmetry Sam Loyd side length small square star strip superposing tessellations swing hinges Swing-and-twist-hingeable dissection swing-hinged dissections symmetry points technique tessellation three squares tion trapezoid truncated octahedron twist twist-hingeable dissection unequal squares vertex wobbly hinged z-square