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
The Return of a Man Called Horse original "A Man Called Horse". Ebert commented that "What gets me is that initiation rite, which is repeated in this film in such grim and bloody detail you'd think people didn't have enough of it the last time. First Morgan has his pectoral muscles pierced with knife blades. Then eagle's talons are drawn through the wounds and tied to leather thongs. Then he hangs by the thongs until sufficiently purified. You'd think one ceremony like that would do the trick, without any booster shots." "The Return of a Man Called Horse" was released to DVD by MGM Home Video on