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
Outer Circle railway line Belgrave and Lilydale lines) with Oakleigh station to the south, via Riversdale on what is now the Alamein line. The final section was north from Riversdale through to Fairfield station (then called Fairfield Park station). There was also a branch line from the closed Waverley Road station (near the modern East Malvern station) to Darling and Burnley. This was the first section of what is now the Glen Waverley line and was opened a few weeks before the Outer Circle. When opened the line was in length, and had 11 stations, all provided with twin platforms and crossing loops. Provision