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
16 - Stardom
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
Harry Lindgren looked up to survey the evening sky: Those millions of points of light were not the ones of his youth. For he had left a homeland of dimmed prospects to seek opportunity “down under.” Each blinking light, which long ago had seemed so small and twinkly, he now knew to represent an object of magnificent size and remarkable structure. And if he were to have surveyed his own life, he might have found a curious resonance.
Denied the chance for postgraduate study in mathematics, he had focused on mathematical recreations. His work on geometric dissections had supernovaed, and he had come to outshine previous luminaries, Henry Dudeney and Sam Loyd included. And when his book was almost finished, he had made a discovery that would ensure his place among the stars. He had found the key to their structure, and with it an elegant new type of dissection, based on simple trigonometric relationships. For us then, he left another sky – his own – full of those beautiful star dissections.
Harry Lindgren's constellations of star dissections take advantage of, and celebrate, the internal structure of polygons and stars first discussed in Chapter 2. He pioneered dissections among pairs of stars and polygons, such that cuts need only be along the sides or diagonals of the constituent rhombuses. Although Geoffrey Mott-Smith (1946) was the first to take advantage of this structure in his dissection of a hexagram to a triangle (Figure 10.21), it was Lindgren who recognized the general principle and used it to create a wealth of what we term auspicious dissections.
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 172 - 186Publisher: Cambridge University PressPrint publication year: 1997