The crossing number of a

knot is the

minimum number of

crossings in any two-dimensional

diagram representing that knot.

The crossing number is a knot invariant. The crossing number of a knot is 0 if and only if it is the unknot. The crossing number of the trefoil is 3.

The span of the Jones Polynomial of an alternating knot is equal to its crossing number. For nonalternating knots, this span is less than or equal to the crossing number.