How Euler Did Even More

Table of Contents

Preface
Part I. Geometry:
1. The Euler line
2. A forgotten Fermat problem
3. A product of secants
4. Curves and paradox
5. Did Euler prove Cramer's Rule?
Part II. Number Theory:
6. Factoring F5
7. Rational trigonometry
8. Sums (and differences) that are squares
Part III. Combinatorics:
9. St Petersburg paradox
10. Life and death – part 1
11. Life and death – part 2
Part IV. Analysis:
12. e, π and i: why is 'Euler' in the Euler identity
13. Multi-zeta functions
14. Sums of powers
15. A theorem of Newton
16. Estimating π
17. Nearly a cosine series
18. A series of trigonometric powers
19. Gamma the function
20. Gamma the constant
21. Partial fractions
22. Inexplicable functions
23. A false logarithm series
24. Introduction to complex variables
25. The Moon and the differential
Part V. Applied Mathematics:
26. Density of air
27. Bending light
28. Saws and modeling
29. PDEs of fluids
30. Euler and gravity
Part VI. Euleriana:
31. Euler and the hollow earth: fact or fiction?
32. Fallible Euler
33. Euler and the pirates
34. Euler as a teacher – part 1
35. Euler as a teacher – part 2
Index
About the author.