As the Planimeter’s Wheel Turns: Planimeter Proofs for Calculus Class
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
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
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
Ricardo Alfaro and Steven Althoen, editors
Descartes Tangent Lines
William Barnier and James Jantosciak
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
This note makes connections between Pell equations, continued fractions, and generalized Fibonacci sequences.
Tennis with Markov
Roman Wong and Megan Zigarovich
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
This note illustrates a recursive approach that yields direct solutions for a class of problems traditionally solved using infinite series.