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
4 - It's Hip to Be a Square
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
The year is 1701. You have just entered the Rose and Crown, a bookshop in St. Paul's Churchyard, London, England. The bookseller, recalling your interest in books scientific and mathematical, pulls out a recent translation of a 1695 book by a German academic, Johann Christoph Sturm: Mathesis Enumerata: or, the Elements of the Mathematicks. “This, esteemed Sir, is a book most handsome. I beseech you: Inspect the many fine figures.” At his behest, you leaf through the thin volume, examining the plates. One of the figures catches your eye: a novel illustration of the Pythagorick Theorem. It places side by side two squares, then cuts them into five pieces that rearrange to form a larger square. Indeed, it is elegant enough to prompt you to review the mathematicks of your purse.
The dissection that caught your eighteenth-century eye is shown in Figure 4.2. It gives a physical realization of a proof of the Pythagorean theorem, which is Proposition 47 of Book I of Euclid's Elements of Geometry. Sturm (1700) produced the illustration, based on a proof by the seventeenth-century Dutch mathematician Frans van Schooten. However, not mentioned in the book is the fact that the dissection is actually much older, having made an appearance eight hundred years before, in Thabit ibn Qurra's Risāla fi'l-hujja al-mansūba ilā Suqrāt fi'l-murabba wa qutrihi (Treatise on the Proof Attributed to Socrates on the Square and Its Diagonals).
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 28 - 39Publisher: Cambridge University PressPrint publication year: 1997