Mathematics Graduate Students Organization

Seminar:

Date: February 27

What is the probability that four points taken at random in the plane will form a convex quadrilateral?

Sylvester posed this problem in the Educational Times in 1864. He believed the the correct answer was 3/4; however, he was surprised to find that there were a variety of different answers with equally valid arguments. These disagreements led to a spirited discussion of what ``at random in the plane'' should mean and helped to motivate the development of geometric probability theory. In this talk, I will discuss the history of Sylvester's Four Point Problem, the theorem that arose from it (with some of the pretty mathematical tools used to prove it), and generalizations of Sylvester's Four Point Problem.