Unexpected Mathematics

One of my favorite aspects of Odd Squad is that the show demonstrates ways mathematical skills and reasoning can be used to solve problems. The show’s mathematical component is embedded in humorous “odd” scenarios, illuminating that math is integrated in our lives away from the Odd Squad screen.

When most people think about daily uses of math, they think about rote calculations—a shopper staying within a budget at the grocery store, a carpenter determining how much wood is needed for a project, or a chef doubling a recipe. However, the places math is hiding and affecting your life may surprise you.

Voting methods have been heavily studied by mathematicians. In the United States, most of our governmental elections are based on a plurality method—the candidate with the most votes wins the election. When there are only two candidates, this method works reasonably well. However, there are many times (14 to be exact) when a gubernatorial candidate has won a governor’s race with a popular vote percentage in the thirties. Angus King was elected governor of Maine in 1994 with only 35% of the popular vote. More notably, former wrestler Jesse Ventura won Minnesota’s 1998 gubernatorial election with less than 37% of the popular vote. In these cases, nearly two-thirds of voters opposed the winner. How would these election outcomes have changed if, instead of only voting for one candidate, voters could have ranked the candidates according to preference? There are many ways votes could be counted with a ranked ballot. In 2016, Maine voters approved a ranked-choice system, known to many mathematicians as plurality with elimination. To demonstrate how this works, let’s suppose that three candidates (A, B, and C) are running in an election. The ranked-votes are cast as follows: 4,000 voters rank A first, B second, and C third; 5,000 voters rank the candidates in the order B, A, C; and 6,000 thousand voters rank C, B, A. In a plurality method, candidate C clearly wins the election (C has 6,000 first-place votes compared to A’s 4,000 and B’s 5,000). However, 10,000 of the 16,000 voters chose candidate C last. If a ranked-choice method had selected the winner, candidate A would be the winner.

As technology continues to evolve, more realistic and advanced video games are designed. Math is behind every aspect of video game design. Applications can clearly be seen when you consider the trajectory a basketball flies through the air in NBA Jam, the slope of the skateboard ramp in Tony Hawk, or the angle the defender takes to attack the ball carrier in a game of Madden Football. However, math is also hiding behind the design of the game and the graphics used to create the scenes. The design of the game play, particularly when chance is involved, is dependent on various probabilities. Figures and scenes are initially broken down into polygons, and the designer’s job of figuring out how these shapes interact takes knowledge of geometry and advanced algebra. The computer programming needed to create the game play requires that the designer have an advanced mathematical basis.

Most of us experience traffic on a regular basis. The main contributors to traffic jams are road congestions, accidents or construction, and poorly timed traffic signals. Mathematicians have been modeling traffic patterns since the mid-1900s, and research in this area has grown as traffic control has become more problematic. Mathematicians use a series of equations to model a vehicle’s position based on the speed limit and the time the car has been driving. These models and equations become much more complex as we consider driver reaction times, space between vehicles, and behavior of fellow drivers. These models have shown that the domino effect of one driver quickly braking can cause a traffic standstill miles down the road. These models have also been used to compute optimal traffic lights settings in large cities.

Next time your candidate loses an election, your friend defeats you in your favorite video game, or you catch all green lights on the way home, you may think it “odd”. However, it really is mathematics at work!

By Dr. Lesley Wiglesworth
Associate Professor of Mathematics

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wiglesworth_entryLesley Wiglesworth joined Centre’s faculty in 2008. She is associate professor of mathematics and was named a Centre Scholar in 2012.

Her research interests are in discrete mathematics and more specifically combinatorics and graph theory. She enjoys studying visibility graphs, a type of graph with applications to circuit layout design. Most recently, Wiglesworth worked on a problem involving the game-acquisition number of graphs with a student at Centre.
She graduated magna cum laude from Transylvania University with a B.A. in mathematics. She earned her M.A. in mathematics and Ph.D. in applied and industrial mathematics from the University of Louisville.

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Categories: Notes from the Faculty, Uncategorized

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