A free-time toy · 30 September 2026
Pull the Knot
Drag the corners. The string won’t pass through itself, so however you pull it, a knot stays that knot. The name on the right is recomputed from scratch after every move.
Things to try
- Turn it. The drawing changes completely and the crossings move, but the name and both polynomials never do.
- Try to undo the trefoil. Pull any corner as far as you like. Strands catch on each other instead of passing through.
- Cheat. Tick “let strands pass through” and drag one strand across another. Now the knot can change, and the name changes with it.
- Load the square knot, then the granny. Their Alexander polynomials are identical. Only the Jones polynomial tells them apart, because it notices handedness.
- “Looks knotted” has 14 crossings from the starting angle. Press “Pull tight” and it falls apart into a triangle.
“Pull tight” deletes any corner whose triangle nothing passes through, which never changes the knot. Handedness follows the usual convention: a trefoil drawn with all crossings negative is left-handed. The mathematics here is a port of the Python used for Knotted by Chance, and the two agreed on all 304 test shapes.