The broadworm problem asks for a planar path C of length 1 for which the minimum width of conv C is as large as possible. We give a construction which quickly shows that there is an extremal path, lying on the boundary of a convex set and symmetric about the perpendicular bisector of the segment joining the endpoints of the path.

As time permits, we will discuss extensions of the following theorem of H. G. Eggleston: Given a triangle T and a closed path C of length s. If s is less than or equal to the circumference of the incircle of T, then T contains a congruent copy of C.