Sorry Fermat, just colouring in the area and putting a 2 on it isn't a solution. Show your work!
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They mentioned the solution: integral sin(x) from x=0 to pi. Doesn't need much explanation
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-cos(π) - (-cos(0)) = 1 - (-1) = 2
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Less intuitive is the solution devised by Holmes Deiter-Westover (1853-1915) when he filled his spacious bathtub in his Dumfries estate. He sloshed back and forth creating huge waves. When asked how many could fit in the tub, he responded, “Two!”
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If from 0 to π the area is 2, what is the length of the curve in that same range?
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To find length of a grach of some function ( in this case it is f(x) = sin(x) ) over some interval ( 0 to pi) you take the integral of square root of sum of square of function’s derivative and 1 over that intervalpic.twitter.com/5JfDwWgDsv
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Really it doesn't matter if the velocity is unity or not, the value of the horizontal distance will be the same and equal to the diameterpic.twitter.com/7cBuNiYSvF
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Area = 1 - (-1) = 2
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Is this made with manim? All hail 3b1b
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