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
There Is a Light That Never Goes Out than that. I was listening to what the Velvet Underground were listening to". AllMusic's Tim DiGravina argues that while depressed characters were a regular feature in Morrissey's work, his lyrics on "There Is a Light" "ups the sad-and-doomed quotient by leaps and bounds." Goddard argues in his book "Songs That Saved Your Life" that the basic narrative story is similar to that of the James Dean film "Rebel Without a Cause", in which Dean—an idol of Morrissey's—leaves his tortuous home life, being the passenger to a potential romantic partner. In fact, a line from that movie ("It is not my