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The 'coastline paradox' is the counterintuitive observation that the coastline of a landmass does not have a well-defined length.
More concretely, the length of the coastline depends on the method used to measure it. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious limit to the size of the smallest feature that should not be measured around, and hence no single well-defined perimeter to the country. Various approximations exist when specific assumptions are made about minimum feature size.
Of course, this might not be a paradox at all once we find for certain the smallest thing there is. It might not be practical to measure a coastline down to the sub-atomic level (particularly since grains of sand are often washed away), but that length would still exist.
For practical considerations, an appropriate choice of minimum feature size is on the order of the units being used to measure. If a coastline is measured in miles, then small variations much smaller than one mile are easily ignored. To measure the coastline in inches, tiny variations of the size of inches must be considered.
Over a wide range of measurement scales, down to the atomic, coastlines show a degree of self-similarity, and as the measurement scale is made smaller and smaller, the measured length continues to increase, rather than converging on any one value. This fractal-like property of natural objects causes the apparent paradox of coastline lengths. ^[1]

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See also

Notes

See also

★ ''How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension''

★ Fractal dimension

★ Paradox of the Heap

Notes

1. The Fractal Geometry of Nature, , Benoit, Mandelbrot, W.H. Freeman and Co., ,