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
22 - Prisms Reformed
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
It was a long commute that summer of 1973: onto the Baltimore Beltway, then Interstate 95, then the Washington Beltway, then into Dupont Circle, and finally the tedious search for free on-street parking. And after 5:00 P.M. I retraced the route in the reverse direction, every day, five days a week. At work, I scrutinized the blueprints of a Long Island hospital to unravel the layout of departments (or were they archduchies?) spread through a maze of interconnected buildings. Sometimes a department extended up through several levels of one building, sometimes it extended across one level in several buildings, and sometimes both. At home, relaxation was afforded by a curious little book of geometrical drawings. And one day, as the symmetries in the dissection of a 10-pointed star and two 5-pointed stars were reflected and refracted in a mind game of what-if, the stars first replicated, then rotated, then stacked as levels of a building, then merged into volumes worthy of those medical potentates.
In this chapter we explore what we can do when planar figures are given thickness, that is, they are turned into right prisms (see Chapter 2). This happens whenever we make a physical model of a planar dissection. We exploit this situation by making cuts parallel to the plane of thickness, as well as perpendicular to it. Of course, our goal is to reduce the number of pieces from the corresponding planar dissection.
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 258 - 267Publisher: Cambridge University PressPrint publication year: 1997