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 non-rectifiable complexes in nature as the infinite coastline. His own definition of the new figure serving as the basis for his study is: