👉 In mathematics, a knot root is a fundamental object that describes the crossing number of knots. It is an integer-valued function on all knots in the 3-sphere S^3, which assigns to each knot its "number of crossings" along its boundary. A knot in S^3 has two types of crossings: self-intersections (which are also called double-crossings) and loops. The number of self-intersections equals the genus of the knot; it is given by the Euler