# Math Help - Curve with no length

1. ## Curve 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.

2. ## Re: 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.

3. ## Re: Curve with no length

Originally Posted by james_bond
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.