Mathematics
Fractal Dimension and the Hausdorff Dimension
Quick fact
The Hausdorff dimension of the Koch snowflake is log 4 / log 3 ≈ 1.2619, meaning it is 'more than a line but less than a plane'.
Why this is interesting
Have you ever wondered whether a coastline has a length? Measure it with a ruler and then with a smaller ruler—you'll get wildly different answers, and the pattern never stops.