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 party Circle line party A Circle line party is a type of subway party occasionally held on the Circle line of the London Underground. Although the time and place of these parties is planned, the event itself occurs spontaneously, as each participant decides for themselves what sort of revelry, costume, decorations, snacks, libations and guests to bring to the party. The participants decorate the carriages festively, and play music, either live or on portable sound systems, disguised to appear as normal luggage. Other activities include setting up pole-dancing poles on the trains. Free drinks, snacks and sweets are provided, often being