Coastline paradox

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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. In a sense, it's like pi: you can round it, but you can't find the full itness of it.

Of course, this might not be a paradox at all once we find for certain the smallest thing there is. It might not be possible 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.

[edit] See also

• How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
• Fractal dimension
• Paradox of the Heap