It turns out it’s quite easy to define a shape that has finite area but infinite perimeter, by giving it finer and finer details at smaller scales (shapes that have finer details at smaller scales like this are called “fractals”). A simple example is the Koch snowflake.

A coastline works a little bit like this. If you calculate the length of a coastline from a world map, you will miss out lots of bays and inlets. If you use a larger scale map, you will take those into account and get a larger value (often much larger) but you will still miss some smaller features. However, once you get down to the smallest length scales, the coastline becomes quite hard to define because of tides and waves. So it’s not exactly a fractal, but it works a little bit like one.

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