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. 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. Content: Prefaces ix 1.Thales of Miletus 1 2.Triangles of Equal Area 3 3.Quadrilaterals 6 4.Perfect Numbers and Triangular Numbers 9 5.The Pythagorean Theorem I