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Last Updated September 21, 2019, 2:46 pm
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The Coastline measurement paradox

This is factoral Mathematics

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The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal-like properties of coastlines, i.e., the fact that a coastline typically has a fractal dimension (which in fact makes the notion of length inapplicable). The first recorded observation of this phenomenon was by Lewis Fry Richardson[1] and it was expanded upon by Benoit Mandelbrot.[2]
The measured length of the coastline depends on the method used to measure it and the degree of cartographic generalization. Since a landmass has features at all scales, from hundreds of kilometres in size to tiny fractions of a millimetre and below, there is no obvious size of the smallest feature that should be taken into consideration when measuring, and hence no single well-defined perimeter to the landmass. Various approximations exist when specific assumptions are made about minimum feature size.
The problem is fundamentally different from the measurement of other, simpler edges. It is possible, for example, to accurately measure the length of a straight, idealized metal bar by using a measurement device to determine that the length is less than a certain amount and greater than another amount—that is, to measure it within a certain degree of confidence or certainty. The more accurate the measurement device, the closer results will be to the true length of the edge. When measuring a coastline, however, the issue is that the result does not increase in accuracy for an increase in measurement —it only increases; unlike with the metal bar, there is no way to obtain a maximum value for the length of the coastline.
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