What is the largest area possible for the convex hull of a path of unit length lying on a plane? For what paths is that largest area attained?



Largest convex hull of a unit length path
The answer seems to be $\frac{1}{2\pi}$, using a semi circle. See 


[Moran, P. A. P. "On a problem of S. Ulam." Journal of the London Mathematical Society 1.3 (1946): 175-179.](http://jlms.oxfordjournals.org/content/s1-21/3/175.full.pdf)


