# Torus knot

Steve Trettel

Medium | Computer generated using a custom-built shader material and THREEjs. |
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The Art | A parameterization of a tubular neighborhood of torus knots, embedded in the 3-sphere. Viewed in 3 dimensional space via stereographic projection through a point on the knot, so that the negative space in the image is homeomorphic to the knot complement. |

The Math | Knot theory is the study of closed loops in 3-dimensional spaces, often in the 3-dimensional sphere. The torus knots are one of the simplest infinite families of knots, defined by wrapping a string around a torus of revolution. The trefoil is the (2,3) torus knot, as it can be formed by wrapping 2 times around a torus in one direction, and 3 in the other. |

Categories | Knot Theory, Computer Graphics, Math Illustration, Stereographic Projection |