Fourier Knots
Abstract
We show that every knot has a checkerbord diagram and that every knot is the closure of a rosette braid. We define Fourier knots of type (n1, n2, n3) as knots which have parametrizations where each coordinate function xi(t) is a finite Fourier series of length ni, and conclude that every knot is a Fourier knot of type (1, 1, n) for some natural number n.
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