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

The prevailing method of estimating a border (or coastline) was to lay off n equal straight-line segments of length ℓ with dividers on a map or aerial photograph. Each end of the segment must be on the boundary. Investigating the discrepancies in border estimation Richardson discovered what is now termed the Richardson Effect: the sum of the segments is inversely proportional to the common length of the segments. In effect, the shorter the ruler, the longer the measured border; thus, the Spanish and Portuguese geographers were using different-length rulers.
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.