Gary writes: << I wrote: << Given integer n > 0, draw a line segment in C connecting each pair of nth roots of unity. Then as n -> oo, does the set of intersection points in C (assume each is given equal weight and the weights sum to 1) approach a continuous density on the unit disk? (Note: we care only about the intersection points, not the rest of the line segments.)
There's a paper on this by Bjorn Poonen and Mike Rubinstein: http://math.berkeley.edu/~poonen/papers/ngon.pdf
That's a fantastic paper based on the theorem they announce; since Bjorn Poonen is one of only about 7 people who ever was in the Top Five in the Putnam Exam *four* times, I don't doubt their result is accurate. But I glanced at each page, and searched for the words "density", "limit" and "limiting" but came up empty. Can anyone find where in the paper it addresses the question of a limiting density? (Also, it appears that one of the references addresses which sets of nth roots of unity add up to 0, a question that arose in this venue not long ago.) Thanks, Dan