  A Tangle is a smooth simple closed curve formed from arcs (or ``links'') of
circles with fixed radius. Most previous study of Tangles has dealt with the
case where these arcs are quarter-circles, but Tangles comprised of thirds and
sixths of circles are introduced. Together, these three families of Tangles are
related to the three regular tilings of the plane by squares, regular hexagons,
and equilateral triangles. This relationship is harnessed to prove results
about the number of links comprising a Tangle and the area that it encloses.
