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by Eugen Jost, Eli Maor
Beautiful Geometry
Cover Page
Title Page
Copyright Page
Dedication Page
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
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Beautiful Geometry
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Copyright Page
Beautiful Geometry
ELI MAOR and EUGEN JOST
Princeton Uxniversity Press
Princeton and Oxford
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