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
Catch points left the main tracks. A derail is another device used for the same purposes as catch and trap points. "Trap points" are found at the exit from a siding or where a secondary track joins a main line. A facing turnout is used to prevent any unauthorised movement that may otherwise obstruct the main line. The trap points also prevent any damage that may be done by a vehicle passing over points not set for traffic joining the main line. In the United Kingdom, the use of trap points at siding exits is required by government legislation. An unauthorised movement