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Problem of the Day #314: $\pi$ January 27, 2012

Posted by Albert in : potd , trackback

Saketh graphs $f(x) = \frac{1}{1+x^2}$ for $x \in [0,1]$. He cuts out the square $0 \leq x \leq 1$, $0 \leq y \leq 1$, then cuts along the line $f(x)$, producing piece 1 (below $f(x)$) and piece 2 (above $f(x)$). He finds that the ratio of the weights of piece 1 to piece 2 is $R$. Given this, help him find an expression for $\pi$.

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