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ARTICLES

**John Todd - Numerical Mathematics Pioneer**

Don Albers

2-23

John Todd, now in his mid-90s, began his career as a pure mathematician, but World War II interrupted that. In this interview, he talks about his education, the significant developments in his becoming a numerical analyst, and the journey that concluded at Caltech. Among the interesting stories are how he met his wife-to-be the mathematician Olga Taussky Todd and how he "saved Oberwolfach."

**As the Planimeter's Wheel Turns: Planimeter Proofs for Calculus Class**

Tanya Leise

24-31

Planimeters are devices that measure the area enclosed by a curve, and they come in a variety of forms. In this article, three of these, the rolling, polar, and radial planimeters, are described, and Green's theorem is used to show why they work.

**Maximizing the Probability of a Big Sweepstakes Win**

Michael W. Ecker

32-36

This article explores the question, "When should you mail in your entries to a sweepstakes in order to have the best chance of winning?"

**An Introduction to Simulated Annealing**

Brian Albright

37-42 An attempt to model the physical process of annealing lead to the development of a type of combinatorial optimization algorithm that takes on the problem of getting trapped in a local minimum. The author presents a Microsoft Excel spreadsheet that illustrates how this works.

**Fallacies, Flaws, and Flimflam**

Ed Barbeau, editor

43-46

**CAPSULES**

Ricardo Alfaro and Steven Althoen, editors

47-57

**Descartes Tangent Lines **

William Barnier and James Jantosciak

47-49

A Descartes tangent line is a tangent line that meets the curve only at the point of tangency. This article answers the question: For *n* a positive integer, is there a polynomial curve that admits exactly *n* Descartes tangent lines?

**Fibonacci-Like Sequences and Pell Equations**

Ayoub B. Ayoub

49-52

This note makes connections between Pell equations, continued fractions, and generalized Fibonacci sequences.

**Tennis with Markov **

Roman Wong and Megan Zigarovich

53-54

Assuming a constant probability for a player to win each point against the opponent in a tennis match, this article uses Markov chains and diagonalization to compute the probability of the player winning a tennis game from deuce. **Tennis (and Volleyball) Without Geometric Series**

Bruce Jay Collings

55-57

This note illustrates a recursive approach that yields direct solutions for a class of problems traditionally solved using infinite series.

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Media Highlights

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Book Reviews