Contents

pp ix-x

Preface

pp xi-xiv

Part I - Geometry

pp 1-2

1 - The Euler Line (January 2009)

pp 3-9

2 - A Forgotten Fermat Problem (December 2008)

pp 10-17

3 - A Product of Secants (May 2008)

pp 18-25

4 - Curves and Paradox (October 2008)

pp 26-31

5 - Did Euler Prove Cramer's Rule? (November 2009—A Guest Column by Rob Bradley)

pp 32-38

Part II - Number Theory

pp 39-40

6 - Factoring F5 (March 2007)

pp 41-44

7 - Rational Trigonometry (March 2008)

pp 45-51

8 - Sums (and Differences) that are Squares (March 2009)

pp 52-58

Part III - Combinatorics

pp 59-60

9 - St. Petersburg Paradox (July 2007)

pp 61-66

10 - Life and Death – Part 1 (July 2008)

pp 67-73

11 - Life and Death – Part 2 (August 2008)

pp 74-80

Part IV - Analysis

pp 81-82

12 - e, π and i: Why is “Euler” in the Euler Identity (August 2007)

pp 83-87

13 - Multi-zeta Functions (January 2008)

pp 88-94

14 - Sums of Powers (June 2009)

pp 95-100

15 - A Theorem of Newton (April 2008)

pp 101-108

16 - Estimating π (February 2009)

pp 109-118

17 - Nearly a Cosine Series (May 2009)

pp 119-123

18 - A Series of Trigonometric Powers (June 2008)

pp 124-131

19 - Gamma the Function (September 2007)

pp 132-135

20 - Gamma the Constant (October 2007)

pp 136-140

21 - Partial Fractions (June 2007)

pp 141-145

22 - Inexplicable Functions (November 2007)

pp 146-153

23 - A False Logarithm Series (December 2007)

pp 154-159