Crossings in Knots

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.

A trefoil knot has 3 crossings.

The knot below has 7 crossings.

Click on the picture to see other 7-crossing knots.

Only the zero knot has a crossing number of zero.

Sometimes you can arrange two knots so that the ropes have the same shape, but when you examine them closely, the strand that crosses over in one knot crosses under at the corresponding crossing in the other knot. Two such knots would not be the same unless they could be further rearranged so that the crossings match. So, keeping track of crossings is important.

An example of two knots that appear the same if you do not examine the crossings too closely are the trefoil knots.

That is why, when you draw pictures or diagrams of knots, you make a break in the line you are drawing (which does not represent a break in the rope) to show that that particular strand of rope crosses under at that crossing.