There exist plenty of mathematical curves whose lengths are undefined. The term to search is "non-rectifiable curve".
This tool is for measuring curves drawn on a piece of paper, not abstract curves.
Oh, that doesn't make it any easier: https://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Brita...
Well, it doesn't in theory, but it does in practice. Natural phenomena are only fractal over a certain range of scales. Outside that range they follow normal rules.
That doesn't fit on a piece of paper, either.
[citation needed]