Cute Young Blonde Girl Reveals On The Rocky Coast At The Sea

The result most astounding to Richardson is that, as ℓ approaches zero, the length of the coastline approaches infinity. Richardson had believed, based on Euclidean geometry, that a coastline would approach a fixed length, as do similar estimations of regular geometric figures. For example, the perimeter of a regular polygon inscribed in a circle approaches the circumference with increasing numbers of sides (and decrease in the length of one side). In Geometric measure theory such a smooth curve as the circle that can be approximated by small straight segments with a definite limit is termed a rectifiable curve.
Describing a coastline
More than a decade after Richardson's work was finished, Benoît Mandelbrot invented a new branch of mathematics, fractal geometry, to describe just such nonrectifiable complexes in nature as the infinite coastline. His own definition of the new figure serving as the basis for his study is:

