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Another invariant is the unknotting number. The unknotting number is the
least number of crossing changes necessary to turn a knot into the
unknot. By "crossing changes" we mean changing the orientation of two
strings where they cross. The trefoil knot can be unknotted by changing
only one crossing from under to over, so the trefoil knot has an
unknotting number of 1.

Supriya Garg
2004-05-02