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
18 - The New Breed
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
Three fat folders lie on the desk. Within each is a series of enthusiastic letters accompanied by a stack of remarkable diagrams. First is the correspondence from a nowdeceased Englishman, second is that from an expatriate Hungarian, and the third is from an expatriate Englishman. Together, these dog-eared and annotated sheets document the origins of a new type of dissection. It has been a wonderful experience to receive these letters, overflowing with new dissections, new ideas, written by new people. They tell the story of expanded boundaries, not merely of countries, not only of dissections, but also of human possibilities. A memorable record, in three fat folders.
The folders are for Stuart Elliott, Alfred Varsady, and Robert Reid; the first two reach back to the late 1970s, and the last commences with a decade-old letter to Martin Gardner. These manila cornucopias chronicle the development of new types of dissections by people who passionately mapped the new terrain. Elliott led off with dissections based on combinations of the relationships discussed in the last two chapters. Soon after, Varsady developed a system of relationships based on decompositions of figures to half-rhombuses. Finally, Reid was drawn into dissections as he whittled down dramatically the number of pieces in many of Elliott's dissections. These three demonstrated that Harry Iindgren's work on the internal structure of polygons and stars could be pushed in exciting new directions.
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 207 - 220Publisher: Cambridge University PressPrint publication year: 1997