Fáry–Milnor theorem

In the mathematical theory of knots, the Fáry–Milnor theorem, named after István Fáry and John Milnor, states that three-dimensional smooth curves with small total curvature must be unknotted. The theorem was proved independently by Fáry in 1949 and Milnor in 1950. It was later shown to follow from the existence of quadrisecants (Denne 2004).

This article is about curvature of knots. For the theorem concerning straight-line embeddings of planar graphs, see Fáry's theorem.
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