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 Again" and the flute section in "There Is a Light That Never Goes Out" (originally written as a guitar part) are based on C# minor arpeggio figure. The song features an ascending F#m–A–B chord sequence that guitarist Johnny Marr took from the Rolling Stones cover of Marvin Gaye's "Hitch Hike". Marr said in 1993 that he included the figure as an "in-joke" to determine if the music press would attribute the inspiration for the part to "There She Goes Again" by the Velvet Underground, who he contended "stole" the figure from "Hitch Hike". Marr commented, "I knew I was smarter