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
Group of rational points on the unit circle Group of rational points on the unit circle In mathematics, the rational points on the unit circle are those points ("x", "y") such that both "x" and "y" are rational numbers ("fractions") and satisfy "x" + "y" = 1. The set of such points turns out to be closely related to primitive Pythagorean triples. Consider a primitive right triangle, that is, with integral side lengths "a", "b", "c", with "c" the hypotenuse, such that the sides have no common factor larger than 1. Then on the unit circle there exists the rational point ("a"/"c", "b"/"c"), which, in the complex plane,