Title: Average plane-size
|University of Waterloo
Abstract: In 1941, Eberhard Melchior proved that, given any finite set of points in the plane, not all on a single line, the average length of a spanned line is at most three. Here a line is spanned if it contains at least two of the given points, and the length of a spanned line is the number given points that it contains. We prove a long-overdue analogue of Melchior's result concerning the average size of spanned planes in three-dimensional Euclidean space. This is joint work with Rutger Campbell and Matthew Kroeker.