Curvature of the Trefoil Knot

move along knot

smoother animation

The blue disk is the osculating circle, also known as the kissing circle or the circle of curvature. The blue vector is in the direction of the principal normal and ends at the center of the osculating circle. It has length

1/κ

, the radius of the osculating circle, where

κ

is the curvature. The red and green vectors are the tangent and binormal vectors of length 2.