Figure 14.

Unknotting numbers. a) Any twist knot has an unknotting number of 1, as inverting one crossing is sufficient to give the unknot 0₁. b) The unknotting number of a torus knot T(p,q) is $1/2$ (p−1)(q−1), In this example, the pentafoil knot 5₁ is converted into a trefoil knot 3₁ by inverting one of its crossings. Changing a second crossing gives the unknot 0₁. So the unknotting number is 2 (=$1/2$ (2−1)(5−1)).