According to Popular Mechanics, the "Coastline Paradox" has been vexing researchers and cartographers since its discovery by mathematician Lewis Fry Richardson in 1951.
The explanation for the paradox is surprisingly simple: unlike human-drawn geometrical shapes, a coastline is full of nooks and crannies made by nature. The more one zooms in on the coastline, the more these inconsistencies multiply. This means that the length of a coastline is completely dependent on what size of measurement unit you use to study it. For example, the coastline of the UK is only 2,800 kilometers long when measured in lengths of 100 kilometers. Shrink that to 50 kilometer measurements and suddenly the coastline is 3,400 kilometers.
Coastlines are like fractals—he further you zoom in, the more complex it gets (famed fractal researcher Benoit Mandelbrot expanded Richardson's work on the paradox). If you were to try to measure a coastline on an atomic level, the length would approach infinity.
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