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 City Circle Line The City Circle Line () or M3 is a future loop line of the Copenhagen Metro. It has been claimed by COWI A/S that the City Circle Line is the largest construction project to have taken place in Copenhagen during the last 400 years. Upon its completion, the network's total length shall be 43km and have 17 stations. Its completion has been anticipated to occur around the summer of 2019. Plans for its construction were approved by the Danish Parliament on 1 June 2007. Preferred bidders were announced during November 2010. The total cost was estimated at