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 Line Stitch Straight Line Stitch Straight Line Stitch is an American metalcore band from Knoxville, Tennessee. Straight Line Stitch initially formed around 2000 and issued an EP and a demo album before adding female vocalist Alexis Brown from Clarksville, Tennessee to the band in 2003. Brown sang on their self-released 2006 effort "To Be Godlike" and then on an EP entitled "The Word Made Flesh" for which they filmed a video for the single "Remission". The video's director, Dale Resteghini, owned the production company Raging Nation Films; in 2007 he formed a subsidiary label of Koch Records called Raging Nation Records, and