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? to the reasons based on race, geography, history and so on. They argue that Renan maintains his intellectual background but subtly, i.e. the arguments he explicitly used in "What is a Nation?" are not consistent with his thinking. The concept of "daily plebiscite" would be ambiguous. They argue that the definition is an opportunist idealization and it should be interpreted within the Franco-Prussian War and in the midst of the dispute concerning the Alsace-Lorraine region. 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