Knot ID (beta)

The Knot ID analysis tools are intended to make it easy to view topological information about curves, whether specified as three dimensional space-curves, two dimensional projections, or standard topological notation. See the About and Documentation pages for more information.

Draw a knot

Visit the drawing tool to draw a knot diagram and view information about its properties.

Torus knots

Enter integers p and q describing a torus knot to view the result and some of its topological properties. p is the number of times the knot winds through the hole of the torus, and q the number of times it winds around the edge.

p and q must (for now) be coprime; this guarantees that the result is a single-component knot.

p =
q =

Upload from file

The format should be three values (x, y, z) per line. For instance, the following would describe a trefoil knot. You can also download this example as a file.

9.0 0.0 0.0
0.781 4.43 2.6
-4.23 1.54 -2.6
-4.5 -7.79 -7.35e-16
3.45 -2.89 2.6
3.45 2.89 -2.6
-4.5 7.79 0.0
-4.23 -1.54 2.6
0.781 -4.43 -2.6

Enter a Gauss code

Visit the dedicated Gauss code page to upload via this standard topological notation.

Upload from paste

The format should be three value (x, y, z) perline, as described in the 'Upload from file' section above. You can copy the given example here to see the knot.