The coastline paradox says coastlines increase in length as measurements get more precise.

As the measuring stick’s length approaches 0, the measurement approaches infinity. Its “real” length is therefore undefined. This is on account of a coastling being fractal—always more surface area the closer you look.rM6

  1. Benoit Mandelbrot, “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” Science 156, no. 3775 (May 5, 1967): 636–38, (See notes.)