Some Publications

A geometrically-themed crossword puzzle appearing in Mathematics Magazine, 90 (2017).


Tic-tac-toe on Affine Planes
Chapter in The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Edited by J. Beineke and J. Rosenhouse, Princeton University Press, 2016.


Indivisibles, Infinitesimals and a Tale of Seventeenth Century Mathematics
In this article, we describe clever arguments by Torricelli and Roberval that employ indivisibles to find the volume of Gabriel's trumpet and the area under the cycloid. We detail 17th century objections to these non-rigorous but highly intuitive techniques as well as the controversy surrounding indivisibles. After reviewing the fundamentals of infinitesimal calculus and its rigorous footing provided by Robinson in the 1960s, we are able to revisit the 17th century solutions. In changing from indivisible to infinitesimal-based arguments, we manage to salvage the beautiful intuition found in these works. (Appears in Mathematics Magazine, 86 (2013).)


Waiting to Turn Left
This paper uses recorded traffic data to examine the Pennsylvania rule for determining the need for dedicated left-turn arrows. (Appears in College Mathematics Journal, 41 (2010).)


Fun and Games with Squares and Planes
Chapter in Resources for Teaching Discrete Mathematics, Edited by B. Hopkins, MAA Notes #74, MAA, 2009.


Stuck in Traffic in Chicago
A writing project for a second-semester calculus class included in the book Writing Projects for Mathematics Courses: Crushed Clowns, Cars, and Coffee to Go, MAA Publications, 2004.


Tic-Tac-Toe on a Finite Plane
Everyone knows how to play tic-tac-toe. On an n x n board, if a player is able to place their marks "n in a row" either horizontally, vertically, or diagonally then they have won the game. What if we keep the rules of the game the same but increase the number of possible lines to include some that would not fit our standard description of "in a row"? We have done this in a systematic way by including only those lines prescribed by a finite affine plane, creating an interesting, geometrically motivated game. We discuss Latin squares and affine planes and the relationship between them in order to describe how the game is played on an affine plane. We also discuss projective planes, showing them as a natural extension of affine planes. Sample tic-tac-toe games on these finite planes are given and the existence of winning and drawing strategies for both players is discussed. (Appears in Mathematics Magazine, 77 (2004).)


Play tic-tac-toe on the affine plane of order 4 by clicking the board below.

The Canadians Should Have Won!?
This paper investigates the problem of determining overall rankings from a panel of voters with varying preferences within the context of the 2002 Olympics pairs figure skating event. (Appears in Math Horizons, X 3 (2003).)


The Wallet Paradox Revisited
In Martin Gardner's "Wallet Game", two players agree to wager the contents of their wallets. The player carrying the lesser amount of money wins the other player's amount. Assuming infinitely repeated trials, we view this game probabilistically and ask if an optimal strategy exists when the distribution of the players' amounts are required to have the same mean. In this paper, we show that no such strategy exists in both the discrete and nonatomic cases. We also consider the analogous restriction on the median. (Appears in Mathematics Magazine, 74 (2001) 378-383.)


Stuck in Traffic in Chicago: A World Wide Web Project
You are caught in bumper-to-bumper traffic heading south to downtown Chicago on Lake Shore Drive. Tuning your radio to the traffic station, you grit your teeth as you hear that the normal fifteen minute commute time from Montrose Street to Randolph Street has been replaced by forty minutes of torture. With all the time on your hands, you start wondering: "How do they calculate traffic times in Chicago?" (This web-based project for calculus students appeared in 2000 and can still be found at the MAA Online: Innovative Teaching Exchange.)

Invariance of the Wilansky Property
In 1991, A. K. Snyder and G. Stoudt identified the Wilansky property as a basis property for a Banach space. In my paper, this property is shown to be invariant with respect to the closed span of the coefficient functionals associated with a basis. (Appears in Analysis, 19 (1999) 327-340.)