Suppose we have three line segments in S: , 2, and 3. We are going to think about projecting these line segments onto planes through the origin, just like we have for knots. (The previous problem allows us to conclude the desired results about knots.) Notice that some projections send an endpoint of a segment and another point on a line to the same point on the plane of projection, which we know makes the projection non-regular. Remember that we are thinking of projections as points on S2, so these non-regular projections (the ones sending a vertex and another point to the same place) form a subset of S. Call this subset N2" ("20" because we are doubling up at a vertex.) Show that N2 is at most a finite union of 1-dimensional curves on S. (In particular, these curves will be the intersection of a plane through the origin and our sphere S.)