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Putnam 1950 B2

Session B

Two obvious approximations to the length of the perimeter of the ellipse with semi-axes $a$ and $b$ are $\pi(a+b)$ and $2 \pi(a b)^{12}$ . Which one comes nearer the truth when the ratio $b / a$ is very close to $1 ?$

Dataset text PutnamGAP. Quoted with source.

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