In mathematics, an Osgood curve is a Jordan curve of positive area. The first example was found by .

Examples of Osgood curves can be produced by slightly modifying one of the constructions of space-filling curve

Space-filling curve

In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square...

s with image the unit square to make it an embedding, though the cost is that it no longer fills the whole unit square.