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
Will the Circle Be Unbroken: Volume Two of "Will the Circle Be Unbroken". Will the Circle Be Unbroken: Volume Two Will the Circle Be Unbroken: Volume Two (also "Circle II") is a 1989 album by the Nitty Gritty Dirt Band. The album follows the same concept as the band's 1972 album, "Will the Circle Be Unbroken", which featured guest performances from many notable country music stars. "Circle II" features largely acoustic, bluegrass music instrumentation with a line-up of contemporary country music artists that includes Johnny Cash, Rosanne Cash, Emmylou Harris, Michael Martin Murphey and Ricky Skaggs. Returnees from the first "Circle" are bluegrass musician Jimmy Martin, banjoist