Cover image for Beautiful Geometry

Beautiful Geometry

Author Eugen Jost , Eli Maor
Release Date: 2014/01/01
ISBN: 9780691150994
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Book Description

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Dedication Page
  5. Contents
  6. Prefaces
  7. 1. Thales of Miletus
  8. 2. Triangles of Equal Area
  9. 3. Quadrilaterals
  10. 4. Perfect Numbers and Triangular Numbers
  11. 5. The Pythagorean Theorem I
  12. 6. The Pythagorean Theorem II
  13. 7. Pythagorean Triples
  14. 8. The Square Root of 2
  15. 9. A Repertoire of Means
  16. 10. More about Means
  17. 11. Two Theorems from Euclid
  18. 12. Different, yet the Same
  19. 13. One Theorem, Three Proofs
  20. 14. The Prime Numbers
  21. 15. Two Prime Mysteries
  22. 16. 0.999… = ?
  23. 17. Eleven
  24. 18. Euclidean Constructions
  25. 19. Hexagons
  26. 20. Fibonacci Numbers
  27. 21. The Golden Ratio
  28. 22. The Pentagon
  29. 23. The 17-Sided Regular Polygon
  30. 24. Fifty
  31. 25. Doubling the Cube
  32. 26. Squaring the Circle
  33. 27. Archimedes Measures the Circle
  34. 28. The Digit Hunters
  35. 29. Conics
  36. 30. 3/3 = 4/4
  37. 31. The Harmonic Series
  38. 32. Ceva’s Theorem
  39. 33. e
  40. 34. Spira Mirabilis
  41. 35. The Cycloid
  42. 36. Epicycloids and Hypocycloids
  43. 37. The Euler Line
  44. 38. Inversion
  45. 39. Steiner’s Porism
  46. 40. Line Designs
  47. 41. The French Connection
  48. 42. The Audible Made Visible
  49. 43. Lissajous Figures
  50. 44. Symmetry I
  51. 45. Symmetry II
  52. 46. The Reuleaux Triangle
  53. 47. Pick’s Theorem
  54. 48. Morley’s Theorem
  55. 49. The Snowflake Curve
  56. 50. Sierpinski’s Triangle
  57. 51. Beyond Infinity
  58. Appendix: Proofs of Selected Theorems Mentioned in This Book
    1. Quadrilaterals
    2. Pythagorean Triples
    3. A Proof That 2 Is Irrational
    4. Euclid’s Proof of the Infinitude of the Primes
    5. The Sum of a Geometric Progression
    6. The Sum of the First n Fibonacci Numbers
    7. Construction of a Regular Pentagon
    8. Ceva’s Theorem
    9. Some Properties of Inversion
  59. Bibliography
  60. Index