  Let S be a triangulated 2-sphere with fixed triangulation T. We apply the
methods of thin position from knot theory to obtain a simple version of the
three geodesics theorem for the 2-sphere [5]. In general these three geodesics
may be unstable, corresponding, for example, to the three equators of an
ellipsoid. Using a piece-wise linear approach, we show that we can usually find
at least three stable geodesics.
