Crossing number

In Knot theory, the crossing number is an example of a knot invariant. A knot's crossing number is simply the lowest number of crossings of any diagram of the knot.

By way of example, the unknot has crossing number zero, the trefoil knot[?] three and the figure eight knot four. There are no other knots with a crossing number this low and just two knots have crossing number 5, but the number of knots with a particular crossing number increases rapidly as we go higher.

Knots (to be precise prime knots[?] are traditionally indexed by crossing number, with a subscript to indicate which particular knot out of those with this many crossings is meant (this sub-ordering is not based on anything in particular). The listing goes 3₁ (the trefoil knot), 4₁ (the figure-eight knot), 5₁, 5₂, 6₁, etc. This order has not changed significantly since P. G. Tait[?] published a tabulation of knots in 1877.