Dissections: Plane & FancyCan you cut an octagon into five pieces and rearrange them into a square? How about turning a star into a pentagon? These are just two of the many challenges of geometric dissections, the mathematical art of cutting figures into pieces that can be rearranged to form other figures, using as few pieces as possible. This book shows you many ingenious ways to solve these problems and the beautiful constructions you can create. This beautifully illustrated book will provide hours of enjoyment for any mathematical puzzle enthusiast. |
Contents
Dat Pussle | 1 |
Our Geometric Universe | 9 |
Fearful Symmetry | 20 |
Its Hip to Be a Square | 28 |
Triangles and Friends | 40 |
All Polygons Created Equal | 51 |
First Steps | 60 |
Step Right Up | 71 |
Curves Ahead | 163 |
Stardom | 172 |
Farewell My Lindgren | 187 |
The New Breed | 207 |
When Polygons Arent Regular | 221 |
On to Solids | 230 |
Cubes Rationalized | 247 |
Prisms Reformed | 258 |
Watch Your Step | 89 |
Just Tessellating | 105 |
Plain OutStripped | 117 |
Strips Teased | 136 |
Tessellations Completed | 150 |
Maltese Crosses | 157 |
Cheated Bamboozled and Hornswoggled | 268 |
Solutions to All Our Problems | 278 |
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| 303 | |
| 307 | |
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Common terms and phrases
6-piece dissection Alfred Varsady angles Chapter Collison's convert corresponding crescent crossposed crossposition cube dashed lines decagon diagonal dimensions dissection Figure dissection in Figure dissection is shown dissection of three dissection puzzles dodecagon dotted lines Dudeney Dudeney's economical dissection eight pieces enneagon equal four pieces gave give Greek Cross Harry Lindgren Henry Dudeney heptagon hexagon hexagrams internal structure isosceles triangle Lindgren 1964b line segments Loyd Loyd's Maltese Cross mathematics method Move/cut left Move/cut right number of pieces octagon P-slide pair parallelogram pentagons pentagram prism problem quadrilateral rearrange rectangle regular polygon Reid's relationship repetition pattern resulting rhombuses right triangle Robert Reid rotational symmetry Sam Loyd shown in Figure side lengths solution star step technique strip superposing T-strip element tessellation element tetrahedron Theobald three pieces three squares tion translational trapezoid truncated octahedron upper left corner Varsady's vertex vertices y-triangle z-square