The Crossing Number of a Knot

Each of the places in a knot where 2 strands touch and one passes over (or under) the other is called a crossing . The number of crossings in a knot is called the crossing number.

Experiment with some knots and their crossing numbers. The zero knot is the only knot which has crossing number zero. But you can twist the zero knot around so that it has crossings in it. What can you say about those crossings to distinguish the zero knot from a different knot with more crossings.

How useful is the crossing number for classifying knots?