Campuses:

Smallest Containers Enclosing Random Equilateral Polygons

Sunday, September 16, 2007 - 5:00pm - 5:15pm
EE/CS 3-180
Eric Rawdon (University of St. Thomas)
Joint work with Akos Dobay, John C. Kern, Kenneth C. Millett,
Michael Piatek,
Patrick Plunkett, and Andrzej Stasiak.


We explore the shape of random polygons by measuring the
average
dimensions of smallest boxes, spheres, and polyhedra that
enclose the
polygons. We present computer simulations to examine the
differences
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
intersect the
scaling profile for phantom polygons. The number of edges at
which
the profiles intersect is known as the equilibrium length with
respect
to the given knot type and spatial measurement. These
equilbrium
lengths are then compared to equilibrium lengths with respect
to other
spatial measurements mentioned here and computed elsewhere.