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
Afterword
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
Needham (1959) gave additional information about the Chinese dissection that estimates π. Anonymous (1897) and Newing (1994) provided evidence of the strain in the relationship of Loyd and Dudeney. The graphics and/or text of Loyd's Sedan Chair Puzzle, Guido Mosaics Puzzle, Mrs. Pythagoras' Puzzle, the Cross and Crescent, the Puzzle of the Red Spade, and The Smart Alec Puzzle are reproduced from (Loyd 1914).
An English translation and commentary for Kepler's polygon tilings appeared in (Field 1979). A biography of Kepler's life with a careful explication of his work can be found in (Caspar 1959), and a survey of Kepler's mathematical contributions is given in (Coxeter 1975). Hogendijk (1984) surveyed early knowledge of the structure of polygons with an odd number of sides. A comprehensive treatment of tessellations and tilings can be found in (Grünbaum and Shephard 1987). See Lines (1935), Coxeter (1963), and Wenninger (1971) for discussions of semiregular polyhedrons. Kepler (1940) first discussed the rhombic dodecahedron, which is also mentioned in (Coxeter 1963).
I rolled out some heavy machinery at the beginning of Chapter 3. Perhaps I should belatedly include a warning by Sir Geoffrey Keynes in (Blake 1967) about interpreting “The Tyger”: “It seems better, therefore, to let the poem speak for itself, the hammer strokes of the craftsman conveying to each mind some part of his meaning Careful dissection will only spoil its impact as poetry.”
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 289 - 292Publisher: Cambridge University PressPrint publication year: 1997