With the tool of tricoloration in hand, one can now prove that knots exist. Shown here is a tricolored trefoil knot, proving that the trefoil is tricolorable. Also shown here is the unknot.
With only one strand in this projection, only one color can be used, but all three colors need to be used for a knot to be tricolorable. Since it has been proven that the Reidemeister moves do not affect tricolorability, there is no ambient isotopy that can make the unknot tricolorable. Thus, there is no way the trefoil knot can be turned into the unknot. Therefore, knots exist!Previous Next