pathological curve
Quick Summary
In mathematics, a pathological curve is one that lacks typical properties of continuous curves. For instance, it might have an undefined tangent at any point, possess infinite length while enclosing a finite area, or have undefinable curvature.1
Examples include the Koch snowflake, which has an infinitely increasing perimeter but a finite enclosed area. Another type is a space-filling curve, which can pass through every point in a given area. These curves are often studied in the field of fractals, which explore self-similarity in mathematical and natural patterns. The Jordan curve theorem deals with simple closed curves, stating they divide a plane into two distinct regions.12
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