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
15 - Curves Ahead
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
My eyes grew rounder as I rolled the microform image forward on the screen. The wording of both the puzzle and its solution differed just enough from the later versions in books to raise a doubt. Perhaps Sam Loyd had not discovered the 6-piece solution to the oval-stool-top puzzle. Perhaps it was sent in by a reader.
Ninety years before, had Loyd's eyes also grown rounder as he examined the reader's letter? Had he been startled to see an improved solution to a puzzle that had become an old saw? Had he wondered what John Jackson, the originator of the puzzle, might have wondered eighty years before? Had Loyd imagined that some day the puzzle might turn into the puzzle of the puzzle, and in a curious way be brought full circle?
John Jackson (1821) posed what may be the earliest published dissection of curved figures. He converted a circular table top (a disk) to the seats of two oval stools with open handholds. His simple 8-piece dissection is shown in Figure 15.1. It has a circular cut centered on, and half the diameter of, the original disk. Two straight cuts, of diameters perpendicular to each other, complete the dissection. Half of the four inner and half of the four outer pieces reassemble to make each stool seat.
Jackson's dissection is not minimal, since Loyd (Inquirer, 1901a) gave the 6-piece dissection in Figure 15.2. The disk is first cut into the two shapes that form the Chinese monad (or Yin and Yang symbol).
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 163 - 171Publisher: Cambridge University PressPrint publication year: 1997