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 a piece of work is a man What a piece of work is a man "What a piece of work is man!" is a phrase within a soliloquy by Prince Hamlet in William Shakespeare's play of the same name. Hamlet is reflecting, at first admiringly, and then despairingly, on the human condition. The soliloquy, spoken in the play by Prince Hamlet to Rosencrantz and Guildenstern in Act II, Scene 2, follows in its entirety. Rather than appearing in blank verse, the typical mode of composition of Shakespeare's plays, the speech appears in straight prose: Hamlet is saying that although humans may appear to think and act "nobly"