Repeat the process. Now repeat the process on each line segment, then repeat the process again, and so on forever. It is infinitely crinkly. Also infinitely long. In fact every piece of the curve, no matter how tiny, is infinitely long.
Length is useless for describing it.
On the other hand, it encloses no area, so area is worthless also. Nowadays we call it a Fractal. There are many ways to define dimension. Curves are measured by length, planar figures by area, or length squared, solid objects by volume, or length cubed. In more general terms Equation 3.