Dividing a circle into areas lines (there are two points on one side and one on the other). So the recurrence can be expressed as which can be easily reduced to using the sums of the first formula_3 natural numbers and the first formula_3 squares, this combines to Finally which yields The lemma asserts that the number of regions is maximal if all "inner" intersections of chords are simple (exactly two chords pass through each point of intersection in the interior). This will be the case if the points on the circle are chosen "in general position". Under this assumption of "generic intersection", the number
Into a Circle March 1988, and reached No. 5 in the chart. Into a Circle embarked on their final tour in September 1989, with Annie Anxiety joining the line-up on backing vocals. The band broke up in October 1989. Hampshire is a member of Thailand-based band Futon, alongside Simon Gilbert (Suede). Jepson later worked as a concert promoter and currently teaches live sound and tour management at the Brighton Institute of Modern Music. Into a Circle Into a Circle (also as In Two a Circle and In2a0) were an English new wave duo, formed in April 1985 by Paul "Bee" Hampshire and Barry