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
Straight from the Desk by Ian Dury and Chaz Jankel, except where indicated. Straight from the Desk Straight from the Desk is a live album by Ian Dury & the Blockheads recorded on 23 December 1978 at the Ilford Odeon, Ilford, East London. There is little information available about the album, other than what can be heard on the record. During the performance of "Billericay Dickie" the audience break the venue's floor, presumably in excitement causing Dury to warn the audience to mind the hole as an introduction to "Hit Me with Your Rhythm Stick" and mention it repeatedly later in the set. Dury