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 line (London Underground) the southern portion of the line. Due to conflict between the two companies it was not until October 1884 that the inner circle was completed. The line was electrified in 1905, and in 1933 the companies were amalgamated into the London Passenger Transport Board. In 1949 the Circle line appeared as a separate line for the first time on the Tube map. In 2009 the closed loop around the centre of London on the north side of the River Thames was broken at Edgware Road and extended west to become a spiral to Hammersmith. The signalling system is being upgraded