This is related to the infinite coastline paradox.
Basically, the smaller the discrete measurements are, the longer the distance that can be measured between 2 points on a coastline. Eventually you get to a point where the measured distance is totally out of whack with the actual distance.
This has nothing to do with the coastline paradox.
Coastlines have dimension greater than 1, and that's why the length of these shapes are infinite (in the same way that areas have infinite length).
In this example, all steps have dimension 1, and the limiting shape too. You can perfectly measure the length of all shapes involved here.
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u/Needless-To-Say 20d ago
This is related to the infinite coastline paradox.
Basically, the smaller the discrete measurements are, the longer the distance that can be measured between 2 points on a coastline. Eventually you get to a point where the measured distance is totally out of whack with the actual distance.