Show that we can find a sequence where equality holds. M is the midpoint of a chord PQ of an ellipse. R is the reals. Hence or otherwise, show that the centroid of any bounded convex open region of the plane is the midpoint of at least three distinct chords of its boundary. Let Q be the set of rationals.
R is the reals.
G is a closed plane curve enclosing a convex region. Let S 0 be a set of points in space. To avoid possible copyright problems, I have changed the wording , but not the substance , of all the problems. Out of print, but available in some university libraries.