Smallest Containers Enclosing Random Equilateral Polygons
Patrick Plunkett, and Andrzej Stasiak.
We explore the shape of random polygons by measuring the
dimensions of smallest boxes, spheres, and polyhedra that
polygons. We present computer simulations to examine the
between these dimensions for polygons with constrained and
unconstrained topology. For each measurement, we find that the
scaling profiles for polygons of a particular knot type
scaling profile for phantom polygons. The number of edges at
the profiles intersect is known as the equilibrium length with
to the given knot type and spatial measurement. These
lengths are then compared to equilibrium lengths with respect
spatial measurements mentioned here and computed elsewhere.