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
Circle MRT line an LRT line that goes from Paya Lebar to Buona Vista via Serangoon and Bishan to form Circle line Stage 3 and 4 in 2001. Circle line Stage 5 was finalised in February 2002 when Stage 4 was extended from Buona Vista to World Trade Centre to close up the link and to provide connectivity from the west to Sentosa, and it became the full Circle line in the end. Stations in Circle line that were a part of the original Marina line plans include Dhoby Ghaut, Bras Basah, Esplanade, Promenade, Nicoll Highway and Stadium. The part of the previously