Trefoil (thing)

The trefoil knot is the first example of a nontrivial knot, that is, it is essentially different from the unknot which is just a circle. Actually there are two of them, the left and right handed trefoils. Here is a picture of a left-handed trefoil knot (reflect in a mirror to get the right handed version).

      /\ /\
     /  \  \
    /  / \  \
   /_ /______\
     /     \
    /_______\

See also knot theory and Jones polynomial for a way to see that the left and right handed trefoils are essentially different (you can't manipulate one into the other without breaking the string).

There is also a plane algebraic curve curve that looks like a trefoil. It has equation
x⁴ +x²y² + y⁴ = x(x² -y²).