Descriptions
The trefoil knot can be defined as the curve obtained from the following parametric equations:
This curve lies entirely on the torus, making the trefoil the simplest example of a torus knot. (Specifically, the trefoil is the (2,3)-torus knot, since the curve winds around the torus three times in one direction and twice in the other direction.)
Any continuous deformation of the curve above is also considered a trefoil knot. Specifically, any curve isotopic to a trefoil knot is also considered to be a trefoil. In addition, the mirror image of a trefoil knot is also considered to be a trefoil. In topology and knot theory, the trefoil is usually defined using a knot diagram instead of an explicit parametric equation.
In algebraic geometry, the trefoil can also be obtained as the intersection in C2 of the unit 3-sphere S3 with the complex plane curve of zeroes of the complex polynomial z2 + w3 (a cuspidal cubic).
A left-handed trefoil and a right-handed trefoil.Read more about this topic: Trefoil Knot
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