Beautiful Geometry

Thales of Miletus -- Triangles of Equal Area -- Quadrilaterals -- Perfect Numbers and Triangular Numbers -- The Pythagorean Theorem I -- The Pythagorean Theorem II -- Pythagorean Triples -- The Square Root of 2 -- A Repertoire of Means -- More about Means -- Two Theorems from Euclid -- Different, yet the Same -- One Theorem, Three Proofs -- The Prime Numbers -- Two Prime Mysteries -- 0.999 -- Eleven -- Euclidean Constructions -- Hexagons -- Fibonacci Numbers -- The Golden Ratio -- The Pentagon -- The 17-Sided Regular Polygon -- Fifty -- Doubling the Cube -- Squaring the Circle -- Archimedes Measures the Circle -- The Digit Hunters -- Conics -- 3/3 = 4/4 -- The Harmonic Series -- Ceva's Theorem -- e -- Spira Mirabilis -- The Cycloid -- Epicycloids and Hypocycloids -- The Euler Line -- Inversion -- Steiner's Porism -- Line Designs -- The French Connection -- The Audible Made Visible -- Lissajous Figures -- Symmetry I -- Symmetry II -- The Reuleaux Triangle -- Pick's Theorem -- Morley's Theorem -- The Snowflake Curve -- Sierpinski's Triangle -- Beyond Infinity -- Appendix: Proofs of Selected Theorems Mentioned in This Book.;"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 acclaimed 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 and beautiful branches of mathematics"-- 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 Acclaimed 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 And Beautiful Branches Of Mathematics-- Thales Of Miletus -- Triangles Of Equal Area -- Quadrilaterals -- Perfect Numbers And Triangular Numbers -- The Pythagorean Theorem I -- The Pythagorean Theorem Ii -- Pythagorean Triples -- The Square Root Of 2 -- A Repertoire Of Means -- More About Means -- Two Theorems From Euclid -- Different, Yet The Same -- One Theorem, Three Proofs -- The Prime Numbers -- Two Prime Mysteries -- 0.999 -- Eleven -- Euclidean Constructions -- Hexagons -- Fibonacci Numbers -- The Golden Ratio -- The Pentagon -- The 17-sided Regular Polygon -- Fifty -- Doubling The Cube -- Squaring The Circle -- Archimedes Measures The Circle -- The Digit Hunters -- Conics -- 3/3 = 4/4 -- The Harmonic Series -- Ceva's Theorem -- E -- Spira Mirabilis -- The Cycloid -- Epicycloids And Hypocycloids -- The Euler Line -- Inversion -- Steiner's Porism -- Line Designs -- The French Connection -- The Audible Made Visible -- Lissajous Figures -- Symmetry I -- Symmetry Ii -- The Reuleaux Triangle -- Pick's Theorem -- Morley's Theorem -- The Snowflake Curve -- Sierpinski's Triangle -- Beyond Infinity -- Appendix: Proofs Of Selected Theorems Mentioned In This Book. Eli Maor And Eugen Jost. Includes Bibliographical References (pages 183-184) And Index. Contents Prefaces. Art through Mathematical Eyes 1. Thales of Miletus 2. Triangles of Equal Area 3. Quadrilaterals 4. Perfect Numbers and Triangular Numbers 5. The Pythagorean Theorem I 6. The Pythagorean Theorem II 7. Pythagorean Triples 8. The Square Root of 2 9. A Repertoire of Means 10. More about Means 11. Two Theorems from Euclid 12. Different, yet the Same 13. One Theorem, Three Proofs 14. The Prime Numbers 15. Two Prime Mysteries 16. 0.999. . . = ? 17. Eleven 18. Euclidean Constructions 19. Hexagons 20. Fibonacci Numbers 21. The Golden Ratio 22. The Pentagon 23. The 17-Sided Regular Polygon 24. Fifty 25. Doubling the Cube 26. Squaring the Circle 27. Archimedes Measures the Circle 28. The Digit Hunters 29. Conics 30. 3/3=4/4 31. The Harmonic Series 32. Ceva’s Theorem 33. e 34. Spira Mirabilis 35. The Cycloid 36. Epicycloids and Hypocycloids 37. The Euler Line 38. Inversion 39. Steiner’s Porism 40. Line Designs 41. The French Connection 42. The Audible Made Visible 43. Lissajous Figures 44. Symmetry I 45. Symmetry II 46. The Reuleaux Triangle 47. Pick’s Theorem 48. Morley’s Theorem 49. The Snowflake Curve 50. Sierpinski’s Triangle 51. Beyond Infinity Appendix: Proofs of Selected Theorems Mentioned in This Book Bibliography Index An exquisite visual celebration of the 2,500-year history of geometry 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.