Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
The Width of a Circle 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 is divided into two