Contest Brings Math, Writing Skills to Forefront

WILMORE, Ky. — By late afternoon on Monday, the jokes were getting a little corny.

“If you were cooking your brownies in a round pan, how would you cut them up? In wedges, like pie?”

“I guess. So in this case, the area of your brownie pan could be calculated using … pie! Or pi. Either one.”

Junior Cali Thomas and senior Aaron Hill concentrate on their math modeling paper.
Junior Cali Thomas and senior Aaron Hill concentrate on their math modeling paper.

The discussion of brownies and pan shapes fit squarely within the realm of academic inquiry as part of Asbury University’s participation in an annual math modeling competition hosted by the Consortium for Mathematics and its Applications (COMAP).

At 8 p.m. on Thursday, five teams of Asbury students got their first look at this year’s problems — one of which involved figuring out various pan/oven configurations for cooking brownies evenly. By 8 p.m. on Monday, each team was responsible for turning in a paper to detail a solution to the problem. The days in between were filled with research, snacks, games … and lots of math.

“Math modeling gives us a real-life experience for professional development,” said senior George Lytle. “There is no textbook solution for the problem, and we work in a team on a deadline. Alumni have come back and said that math modeling is the most true-to-life experience they have as undergraduates.”

Once the papers are completed and edited, they are mailed to COMAP, where a panel of judges that includes mathematicians, math educators and others who work in fields directly related to mathematics, reviews each paper. Contest results are available later in the spring; in the past, Asbury teams have been counted in the top 15 percent of the 3,000+ entries received each year from around the world.

Can you take the heat?

Here’s a taste of this year’s math modeling problems:

PROBLEM A: The Ultimate Brownie Pan

When baking in a rectangular pan, heat is concentrated in the four corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge, and the product is not overcooked at the edges. However, since most ovens are rectangular in shape, using round pans is not efficient with respect to using the space in an oven. Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.

Assume

1. A width to length ratio of W/L for the oven which is rectangular in shape.

2. Each pan must have an area of A.

3. Initially two racks in the oven, evenly spaced.

Develop a model that can be used to select the best type of pan (shape) under the following conditions:

1. Maximize number of pans that can fit in the oven (N)

2. Maximize even distribution of heat (H) for the pan

3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.

In addition to your solution, prepare a one- to two-page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.

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