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
Area of a circle approximation among rational numbers with denominator up to 113. The number ⁄ is also an excellent approximation to , better than any other rational number with denominator less than 16604. Snell proposed (and Huygens proved) a tighter bound than Archimedes': This for "n" = 48 gives a better approximation (about 3.14159292) than Archimedes' method for "n" = 768. Let one side of an inscribed regular "n-"gon have length "s" and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle