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
Outer Circle railway line Belgrave and Lilydale lines) with Oakleigh station to the south, via Riversdale on what is now the Alamein line. The final section was north from Riversdale through to Fairfield station (then called Fairfield Park station). There was also a branch line from the closed Waverley Road station (near the modern East Malvern station) to Darling and Burnley. This was the first section of what is now the Glen Waverley line and was opened a few weeks before the Outer Circle. When opened the line was in length, and had 11 stations, all provided with twin platforms and crossing loops. Provision