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
City Circle Line areas of Copenhagen, including the Danish Parliament, the Central Station, City Hall, and multiple stations of the S-train and existing metro stops. Access to the region and commuter heavy rail network is also deliberately provision for at several places along its route; furthermore, a twin-track line is to provide a connection between the City Circle Line and the Nordhavnen Metro. Just as M1 and M2 share a section of the existing metro, the City Circle Line will share a 6-station section with the future M4 line. Initially, two possible routes were considered, after an even bigger screening of ideas. During