## Math Room Fun at the Fall Science Open House

Posted: Wednesday, January 9, 2013

The Department of Mathematics joined the departments of astronomy, chemistry, geology, and physics for the first time last fall in the College of Arts and Sciences' annual science open house, held on October 22, 2012. Math faculty and graduate students entertained and informed the many visitors. Mathematics' first-time participation was spearheaded by Professor Matthias Weber.

The Math Room featured three activities: The main focus was the game Dots and Boxes. Many of the participants knew the game already. Math staff surprised players by teaching them to play a much stronger game by using counting arguments. This was done on a one-on-one basis with specially trained graduate students and faculty.

A second activity involved a hands-on version of the following problem: Three pitchers hold precisely 3, 5, and 8 gallons of water. The pitchers are without markings and irregularly shaped. The 8 gallon pitcher is full. By pouring water from one pitcher into another (always to the rim), the player tries to divide the water so that two pitchers contain 4 gallons each. This best solution takes 7 pourings. While it looks like this problem requires a trial and error approach, the interested player learned that there is a clever way of finding the solution by playing billiards on a billiard table in the shape of a parallelogram.

The third activity explained the design of this year's Open House t-shirt, which showed a circle with several lines in it that traced an ellipse within the circle. To make such a design, draw a circle on a sheet of paper and mark a point within the circle (but not the center). Then fold the paper so that a point on the perimeter of the circle is folded onto the marked point. Unfold, and repeat this a few times with other points on the perimeter. The result will look similar to the t-short logo.

Samuel N. Rosenberg (translator)