Shenandoah Undergraduate Mathematics and Statistics Conference
at James Madison University, October 18, 2008
Opening Address
Sufferin' Succotash! A Problem of Sylvester's
Michael Mossinghoff
University of South Carolina and Davidson College
| Abstract:
Suppose a finite number of points are placed in the plane in such a way
that they do not all lie on the same line. Must there exist a line that
connects exactly two of the
points? Suppose each of the points are then colored red or blue in some way. Must there exist a line that joins two or more points of one color, but intersects none of the other color? Can you always join exactly two points of one color and none of the other? Does anything change if you have an infinite number of points? We'll investigate these questions, some of which were raised more than a century ago by the British mathematician James Joseph Sylvester. We'll describe some novel methods used to investigate these problems, and discuss several interesting results, including some contributions made by undergraduate students. Biography:
Michael Mossinghoff has a Ph.D. in mathematics from the University of
Texas at Austin, and a master's degree in computer science from
Stanford University. After teaching at Appalachian State
University and at UCLA, he joined the faculty at Davidson College in
2002, where he teaches mathematics and computer science. For the
current academic year, he is a |