Examples for

Knot Theory

In topology, knot theory is about the study of knots and their properties, where a knot is defined as a closed, non-self-intersecting curve embedded in three-dimensional space. Wolfram|Alpha has the ability to recognize a knot with multiple representations and compute its properties or to compare multiple knots.

Knots

Find and visualize a knot, either by its common name or by using knot notations.

Compute properties of a knot:

trefoil knot

Miller Institute knot

Specify a knot using Alexander–Briggs notation:

8_1 knot

Specify a knot using Conway notation:

Conway 21112 knot

Compute properties of a torus knot:

2,5 torus knot

Compare several knots:

Stevedore knot, figure eight knot

Compute a specific property of a knot:

What is the HOMFLY polynomial of the figure eight knot?

More examples