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Suppose $\alpha$ is a Jordan curve. Suppose $\beta$ is another Jordan curve such that $\alpha$ is contained in the region limited by $\beta$.

Maybe it is an easy question, but, how can one show that the length of $\beta$ is bigger than or equal to the length of $\alpha$?

Is the length of $\beta$ equal to length of $\alpha$ if and only if $\alpha=\beta$?

Thanks

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You cannot. In fact, $\alpha$ can be as wiggly as you want, even having infinite length, while $\beta$ has finite length.

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    i dont believe it, hahha, therefore i couldnt find an easy demonstration.2012-10-23