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).

A three-leaved clover representing the three parts of the Girl Scout Promise. Also a very yummy shortbread Girl Scout Cookie.

Tre"foil (?), n. [L. tres three + E. foil leaf; cf. F. frefle, It. trifoglio, L. trifolium. See Tri-, Foil leaf, and cf. Trifoly.]

1. Bot.

Any plant of the genus Trifolium, which includes the white clover, red clover, etc.; -- less properly, applied also to the nonesuch, or black medic. See Clover, and Medic.

2. Arch.

An ornamental foliation consisting of three divisions, or foils.

3. Her.

A charge representing the clover leaf.

 

© Webster 1913.

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