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
Fife Circle Line Fife Circle Line The Fife Circle is the local rail service north from Edinburgh. It links towns of south Fife and the coastal towns along the Firth of Forth before heading to Edinburgh. Operationally, the service is not strictly a circle route, but, rather, a point to point service that reverses at the Edinburgh end, and has a large bi-directional balloon loop at the Fife end. The service includes the Edinburgh-Dunfermline stretch of the East Coast Main Line, which includes the world-famous Forth Bridge. On the Fife side, while this line hugs the coast, the circle is formed by a