Published online by Cambridge University Press: 20 November 2018
Banchoff and Pohl [3] have proved the following generalization of the isoperimetric inequality.
Theorem. If γ is a closed, not necessarily simple, planar curve of length L, and w(p) is the winding number of a variable point p with respect to γ, then
1
with equality holding if and only if γ is a circle traversed a finite number of times in the same sense.