Hi!

I am asked to find some curves which don't have length. I'm not sure whether the Koch curve is appropriate as it has infinite length.

Thanks for your help!

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- Oct 23rd 2011, 08:35 AMjames_bondCurve with no length
Hi!

I am asked to find some curves which don't have length. I'm not sure whether the Koch curve is appropriate as it has infinite length.

Thanks for your help! - Nov 5th 2011, 07:15 AMTinybossRe: Curve with no length
You could also look at "space-filling curves". But really they're just other (maybe we can say "worse") examples of curves with infinite length. The term is "non-rectifiable".

Since length is defined as the integral of the magnitude of the derivative, any curve which fails to be differentiable on a set of positive measure won't have a defined length. - Nov 5th 2011, 10:25 PMCaptainBlackRe: Curve with no length
The usal example of a function that is nowhere differentiable is the Blancmange function

CB