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
Circle of Two like Laurence Olivier, for his willingness to do anything for money. He stooped so low in 1981 as to appear in Jules Dassin’s "Circle of Two", in which he plays a 60-year-old artist who falls for the 16-year-old Tatum O’Neal. By the time of his death three years later, his artistic reputation was in tatters. Circle of Two Circle of Two is a 1981 Canadian drama film starring Richard Burton as a 60-year-old artist who lost his inspiration when his muse left him 10 years previously, who regains it when he falls in love with a sixteen-year-old played by Tatum