CONSTRUCTION OF A LATTICE KNOT WHOSE THREE SHADOWS ARE ALL TREES

It is known by few that a trivial knot can be transformed into a lattice knot whose three shadows are all trees (here, three shadows mean the projections of the lattice knot to the directions of ordinary orthogonal axes). Since a knot itself is a loop in the space, this fact may be rather astonishing. It will be interesting to ask whether a non-trivial knot has such a transformation or not. The purpose of this paper is to show that any two-bridge torus knot or link has a transformation into a lattice knot whose three shadows are all trees. The algorithm to construct such a position will be demonstrated.