X-Nico

4 unusual facts about Trefoil knot


Arf invariant of a knot

Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent.

Homotopy

The unknot is not equivalent to the Trefoil knot since one cannot be deformed into the other through a continuous path of embeddings.

Space Harmony

The patterns of many scales can be found to be based on the Trefoil knot.

Torus knot

Unknot, 171 knot (7,2), 819 knot (4,3), 91 knot (9,2), 10124 knot (5,3)



see also