Mathematical Time Capsules

Preface; Part I: 1. The sources of algebra Roger Cooke; 2. How to measure the Earth Lawrence D'Antonio; 3. Numerical solution of equations Roger Cooke; 4. Completing the square through the millennia Dick Jardine; 5. Adapting the medieval 'rule of double false position' to the modern classroom Randy K. Schwartz; 6. Complex numbers, cubic equations and sixteenth-century Italy Daniel J. Curtin; 7. Shearing with Euclid Davida Fischman and Shawnee McMurran; 8. The mathematics of measuring time: the sinking-bowl water-clock in India Kim Plofker; 9. Clear sailing with trigonometry: navigating the seas in fourteenth-century Venice Glen Van Brummelen; 10. Copernican trigonometry Victor Katz; 11. Cusps: horns and beaks Robert E. Bradley; 12. The latitude of forms area and velocity Daniel J. Curtin; 13. Descartes' approach to tangents Daniel J. Curtin; 14. Integration a la Fermat Amy Shell-Gellasch; Interlude: 15. Sharing the fun: student presentations Amy Shell-Gellasch and Dick Jardine; 16. Web searches and scavenger hunts: letting students dig up history Betty Mayfield; 17. Newton vs. Leibniz in one hour! Betty Mayfield; Part II: 18. Connections between Newton, Leibniz, and Calculus I Andrew B. Perry; 19. A different sort of calculus debate Vicky Williams Klima; 20. A symbolic history of the derivative Clemency Montelle; 21. Leibniz's calculus (real retro calc) Robert Rogers; 22. An 'impossible' problem, courtesy of Leonhard Euler Homer S. White; 23. Multiple representations of functions in the history of mathematics Robert Rogers; 24. The unity of all science: Karl Pearson, the mean, and the standard deviation Joe Albree; 25. Finding the greatest common divisor and more. J. J. Tattersall; 26. Negativo-affirmative figures and an alternative technique for multiplying two numbers J. J. Tattersall; 27. Origins of the integrating factor Dick Jardine; 28. Euler's method in Euler's words Dick Jardine; 29. Newton's differential equation y/x=1-3x+y+xx+xy Huseyin Kocak; 30. Roots, rocks, and Newton-Raphson algorithms for approximating 3000 years apart Clemency Montelle; 31. Plimpton 322: the Pythagorean Theorem, more than a thousand years before Pythagoras Daniel E. Otero; 32. Thomas Harriot's Pythagorean Triples: could he list them all? Janet L. Beery; 33. Amo, Amas, Amat! What's the sum of that? Bernoulli's account of the divergent harmonic series in Latin Clemency Montelle; 34. The harmonic series: a primer Adrian Rice; 35. Learning to move with Dedekind Fernando Q. Gouvea.