How Euler Did Even More

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.