On Thu, 2 Feb 2006 dasimov@earthlink.net 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.)
Consider the set C(n) of points in the plane obtained by intersecting all line segments joining the n-th roots of unity. Then plot as a single picture the set D(n) = union of C(k) for k from 3 to n. Why should the face of a monkey appear in D(25)? If you can read postscript (or eps) files you can see the Maple generate picture of this set here: http://www.math.usf.edu/~eclark/D25.eps --Edwin