Efnisyfirlit

• Title
• Copyright
• Dedication
• Contents
• Prefaces
• 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
• Quadrilaterals
• Pythagorean Triples
• A Proof That √2 Is Irrational
• Euclid’s Proof of the Infinitude of the Primes
• The Sum of a Geometric Progression
• The Sum of the First n Fibonacci Numbers
• Construction of a Regular Pentagon
• Ceva’s Theorem
• Some Properties of Inversion
• Bibliography
• Index