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Any curve can be considered to be made of sufficiently small straight lines. What is the name of the theorem which states this fact?

Thank you.

I asked the same question at Hacker News.

[Edit: in the Hacker News question, the OP included the following link, which I think clarifies his/her intent:

http://musr.physics.ubc.ca/~jess/hr/skept/Math/node10.html

--PLC.]

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    Can it, really?2010-10-05
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    Let's be a little generous and perhaps offer assumptions needed for this to have a meaningful interpretation and to be true, recognizing that it comes from a non-mathematician seeking help. E.g., "all piecewise differentiable curves are rectifiable."2010-10-05
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    Is any curve "piecewise differentiable"? Is any rectifiable curve "made of sufficiently small straight lines"?2010-10-05
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    I started a discussion about this on meta because I would like it re-opened if possible.2010-10-05
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    On the assumption that it is useful to have a permanent link to the relevant discussion on meta posted here: http://meta.math.stackexchange.com/questions/901/request-for-reopening-equivalence-of-curved-and-straight-lines2010-10-05
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    It took so long with the closing and reopening, I don't even know if Zeynel is following this question now!2010-10-21

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