Osgood curve

Not to be confused with the Ramberg–Osgood curve relating stress to strain in material science.
Example of an Osgood curve, constructed by recursively removing wedges from triangles. The wedge angles shrink exponentially, as does the fraction of area removed in each level, leaving nonzero area in the final curve.

In mathematical analysis, an Osgood curve is a non-self-intersecting curve that has positive area. Despite its area, it is not possible for such a curve to cover any two-dimensional region, distinguishing them from space-filling curves. Osgood curves are named after William Fogg Osgood.