Trefoil Knot

The trefoil knot is the simplest non-trivial knot in three-dimensional space: it cannot be deformed into a circle without cutting, yet it can be drawn with only three crossings. It is the (2, 3)-torus knot and the closure of the simplest non-trivial braid. Knot theory grew out of Lord Kelvin's 19th-century attempt to model atoms as knotted ether vortices, and has since become a thriving branch of low-dimensional topology with applications to DNA biology and quantum field theory.

The parameterization combines \sin(t), \sin(2t), \cos(t), \cos(2t), and \sin(3t) over 0 \le t \le 2\pi, producing the characteristic three-fold symmetry. A thick glass-like stroke makes the over-and-under structure of the crossings legible as the path closes back on itself. The mirror image of this knot is also a trefoil, but the two are not deformable into each other, making the trefoil the simplest example of a chiral knot.