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
What Is a Nation? What Is a Nation? "What is a Nation?" ("Qu'est-ce qu'une nation?") is an 1882 lecture by French historian Ernest Renan (1823–1892), known for the statements that a nation is "a daily referendum", and that nations are based as much on what the people jointly forget, as what they remember. It is frequently quoted or anthologized in works of history or political science pertaining to nationalism and national identity. Renan wrote "What is a Nation" in order to symbolize the nationalism which was born in France as a result of the French Revolution of 1789. Renan begins his essay by noting