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 the band's "comeback" record. However, Johnny Marr was insistent that "Bigmouth Strikes Again" be the band's next single. Despite Travis's advocation of the song, Simon Goddard expressed doubt that the song's "explicit glamorisation of suicide" would have endeared it to daytime radio. Regardless, "There Is a Light That Never Goes Out" became the second Smiths song to top BBC Radio One disc jockey John Peel's Festive Fifty poll in his 1986 tally. The song was shortly thereafter included on the 1987 compilation album "The World Won't Listen". In October 1992, "There Is a Light That Never Goes Out" finally received