Dividing a circle into areas "F" can also be derived, which will solve the problem. Its vertices include the "n" points on the circle, referred to as the exterior vertices, as well as the interior vertices, the intersections of distinct chords in the interior of the circle. The "generic intersection" assumption made above guarantees that each interior vertex is the intersection of no more than two chords. Thus the main task in determining "V" is finding the number of interior vertices. As a consequence of the lemma, any two intersecting chords will uniquely determine an interior vertex. These chords are in turn uniquely determined by
Curvature of a measure points "x", "y" and "z" in R, let "R"("x", "y", "z") be the radius of the Euclidean circle that joins all three of them, or +∞ if they are collinear. The Menger curvature "c"("x", "y", "z") is defined to be with the natural convention that "c"("x", "y", "z") = 0 if "x", "y" and "z" are collinear. It is also conventional to extend this definition by setting "c"("x", "y", "z") = 0 if any of the points "x", "y" and "z" coincide. The Menger-Melnikov curvature "c"("μ") of "μ" is defined to be More generally, for "α" ≥ 0, define "c"("μ")