Book contents
- Frontmatter
- Contents
- Preface
- 1 “Dat Pussle”
- 2 Our Geometric Universe
- 3 Fearful Symmetry
- 4 It's Hip to Be a Square
- 5 Triangles and Friends
- 6 All Polygons Created Equal
- 7 First Steps
- 8 Step Right Up!
- 9 Watch Your Step!
- 10 Just Tessellating
- 11 Plain Out-Stripped
- 12 Strips Teased
- 13 Tessellations Completed
- 14 Maltese Crosses
- 15 Curves Ahead
- 16 Stardom
- 17 Farewell, My Lindgren
- 18 The New Breed
- 19 When Polygons Aren't Regular
- 20 On to Solids
- 21 Cubes Rationalized
- 22 Prisms Reformed
- 23 Cheated, Bamboozled, and Hornswoggled
- 24 Solutions to All Our Problems
- Afterword
- Bibliography
- Index of Dissections
- General Index
9 - Watch Your Step!
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 “Dat Pussle”
- 2 Our Geometric Universe
- 3 Fearful Symmetry
- 4 It's Hip to Be a Square
- 5 Triangles and Friends
- 6 All Polygons Created Equal
- 7 First Steps
- 8 Step Right Up!
- 9 Watch Your Step!
- 10 Just Tessellating
- 11 Plain Out-Stripped
- 12 Strips Teased
- 13 Tessellations Completed
- 14 Maltese Crosses
- 15 Curves Ahead
- 16 Stardom
- 17 Farewell, My Lindgren
- 18 The New Breed
- 19 When Polygons Aren't Regular
- 20 On to Solids
- 21 Cubes Rationalized
- 22 Prisms Reformed
- 23 Cheated, Bamboozled, and Hornswoggled
- 24 Solutions to All Our Problems
- Afterword
- Bibliography
- Index of Dissections
- General Index
Summary
Standing to one side of the soap box, the clown sports a greasepaint smirk on his face. On the box is printed the label Washington Soap – Free From Lye. Could this be a satiric political cartoon from the closing years of the twentieth century? No, this is the illustration accompanying a Sam Loyd math puzzle from the opening years of that same century.
Did you watch your step, you puzzled masses of the modern age? For you needed the same good measure of skepticism to solve that puzzle that our fed-up-and-nottaking- it-anymore citizenry now need to cut through all the splattered mud and political hocus-pocus. For Loyd had set the seemingly impossible task of dissecting a three-dimensional box to a two-dimensional square. If he himself had been on the square, he should have admitted that he intended that the projected outline of the box be dissected. And not to give away anything to modern trickery, a row of crooked steps was needed to solve the puzzle in the required two pieces!
The politic puzzling – or is it puzzle politicking? – that we indulge in here was prompted by the Jack and the Box Puzzle published by Loyd (Press, 1902b). We reproduce a facsimile of the box in Figure 9.1. To trip up his readers, Loyd used a modified form of the familiar step technique so that the required steps were not at right angles to each other.
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 89 - 104Publisher: Cambridge University PressPrint publication year: 1997