Area of a circle trigonometry, uses the coarea formula. Define a function formula_10 by formula_11. Note ρ is a Lipschitz function whose gradient is a unit vector formula_12 (almost everywhere). Let "D" be the disc formula_13 in formula_14. We will show that formula_15, where formula_16 is the two-dimensional Lebesgue measure in formula_14. We shall assume that the one-dimensional Hausdorff measure of the circle formula_18 is formula_19, the circumference of the circle of radius "r". (This can be taken as the definition of circumference.) Then, by the coarea formula, Similar to the onion proof outlined above, we could exploit calculus in a different way in
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"