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 line party Circle line party A Circle line party is a type of subway party occasionally held on the Circle line of the London Underground. Although the time and place of these parties is planned, the event itself occurs spontaneously, as each participant decides for themselves what sort of revelry, costume, decorations, snacks, libations and guests to bring to the party. The participants decorate the carriages festively, and play music, either live or on portable sound systems, disguised to appear as normal luggage. Other activities include setting up pole-dancing poles on the trains. Free drinks, snacks and sweets are provided, often being