  I show that every rectifiable simple closed curve in the plane can be
continuously deformed into a convex curve in a motion which preserves arc
length and does not decrease the Euclidean distance between any pair of points
on the curve. This result is obtained by approximating the curve with polygons
and invoking the result of Connelly, Demaine, and Rote that such a motion
exists for polygons. I also formulate a generalization of their program,
thereby making steps toward a fully continuous proof of the result. To
facilitate this, I generalize two of the primary tools used in their program:
the Farkas Lemma of linear programming to Banach spaces and the Maxwell-Cremona
Theorem of rigidity theory to apply to stresses represented by measures on the
plane.
