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 Width of a Circle David Bowie" in 1974. The Width of a Circle "The Width of a Circle" is a song written by David Bowie in 1969 for the album "The Man Who Sold the World", recorded in Spring 1970 and released later that year in the United States and in April 1971 in the UK. It is the opening track to the album, a hard rocker with heavy metal overtones. Bowie had performed a shorter version of the song in concerts for several months before recording it. Featuring Mick Ronson's lead guitar work and occasional choral effects from the band, this 8-minute song