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 home") is quoted in the song. According to Goddard, an earlier version lacked some of the finished version's ambiguity, culminating in the line "There is a light "in your eyes" and it never goes out". Due to a dispute between the Smiths and its record label Rough Trade Records after the group completed "The Queen Is Dead", nine months passed after the release of "The Boy with the Thorn in His Side" before the group issued another single. Once the matter was resolved, Rough Trade owner Geoff Travis felt that "There Is a Light That Never Goes Out" should be