University Calendar

Cihan Karabulut, William Patterson University, presents this seminar.

Let L denote the lattice N x N. A point (r, s) in L is called visible from the origin, or simply visible, if it lies on a straight line through the origin (0, 0) and no other lattice point lies on this line of sight between (0, 0) and (r, s). Given this definition, it is natural to ask what proportion of lattice points are visible from the origin, which is equivalent to computing the probability that two integers are relatively prime. This problem was first addressed in the 1800s by numerous people including: Dirichlet, Cesàro and Sylvester. In this talk, we will investigate this question and its recent generalizations to other lines of sight. This is joint work with Jorge Flórez.