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Tales of Impossibility
CHAPTER 15. Descartes’s Compass-and- Straightedge Arithmetic
monograph
Publication date:
December 31 2019
Publisher:
Princeton University Press
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Author and book information
Book Chapter
Publication date:
December 31 2019
Pages
: 233-253
DOI:
10.1515/9780691194233-017
SO-VID:
1ee62dec-dfa2-43e7-a12e-fda192972b10
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Book chapters
pp. i
Front Matter
pp. i
Frontmatter
pp. vii
Contents
pp. vii
Table of Contents
pp. xi
Preface
pp. xi
Preface
pp. 1
Introduction
pp. 1
Introduction
pp. 7
The Four Problems
pp. 7
CHAPTER 1. The Four Problems
pp. 18
TANGENT:
pp. 25
CHAPTER 1. The Four Problems
pp. 25
Proving the Impossible
pp. 34
TANGENT:
pp. 38
CHAPTER 3. Compass-and- Straightedge Constructions
pp. 38
Compass-and-Straightedge Constructions
pp. 55
TANGENT:
pp. 56
CHAPTER 4. The First Mathematical Crisis
pp. 56
The First Mathematical Crisis
pp. 67
TANGENT:
pp. 69
CHAPTER 5. Doubling the Cube
pp. 69
Doubling the Cube
pp. 80
TANGENT:
pp. 81
CHAPTER 6. The Early History of π
pp. 81
The Early History of 𝜋
pp. 93
TANGENT:
pp. 95
Quadratures
pp. 95
CHAPTER 7. Quadratures
pp. 105
TANGENT:
pp. 108
CHAPTER 8. Archimedes’s Number
pp. 108
Archimedes’s Number
pp. 130
TANGENT:
pp. 137
CHAPTER 9. The Heptagon, the Nonagon, and the Other Regular Polygons
pp. 137
The Heptagon, the Nonagon, and the Other Regular Polygons
pp. 144
TANGENT:
pp. 146
CHAPTER 10. Neusis Constructions
pp. 146
Neusis Constructions
pp. 157
TANGENT:
pp. 160
Curves
pp. 160
CHAPTER 11. Curves
pp. 174
TANGENT:
pp. 178
Getting By with Less
pp. 178
CHAPTER 12. Getting By with Less
pp. 192
TANGENT:
pp. 196
CHAPTER 13. The Dawn of Algebra
pp. 196
The Dawn of Algebra
pp. 215
TANGENT:
pp. 219
Viète’s Analytic Art
pp. 219
CHAPTER 14. Viète’s Analytic Art
pp. 228
TANGENT:
pp. 233
CHAPTER 15. Descartes’s Compass-and- Straightedge Arithmetic
pp. 233
Descartes’s Compass-and-Straightedge Arithmetic
pp. 251
TANGENT:
pp. 254
CHAPTER 16. Descartes and the Problems of Antiquity
pp. 254
Descartes and the Problems of Antiquity
pp. 263
TANGENT:
pp. 268
Seventeenth-Century Quadratures of the Circle
pp. 268
CHAPTER 17. Seventeenth- Century Quadratures of the Circle
pp. 279
TANGENT:
pp. 288
CHAPTER 18. Complex Numbers
pp. 288
Complex Numbers
pp. 300
TANGENT:
pp. 302
Gauss’s 17-gon
pp. 302
CHAPTER 19. Gauss’s 17-gon
pp. 316
TANGENT:
pp. 320
CHAPTER 20. Pierre Wantzel
pp. 320
Pierre Wantzel
pp. 342
TANGENT:
pp. 348
CHAPTER 21. Irrational and Transcendental Numbers
pp. 348
Irrational and Transcendental Numbers
pp. 366
TANGENT:
pp. 367
EPILOGUE. Sirens or Muses?
pp. 367
EPILOGUE:
pp. 369
Notes
pp. 369
Notes
pp. 405
References
pp. 405
References
pp. 429
Index
pp. 429
Index
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