Constructing a polynomial whose nodal set is the three-twist knot 5<sub>2</sub>
Constructing a polynomial whose nodal set is the three-twist knot 5<sub>2</sub>
We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain …