The idea is that the film will minimise the area of the surface of revolution given bydA= 2r(s)1+r'(s)2 ds,where r(s) is the surface's radius from the rings' centre, and s parameterises the distance coordinate between them. Minimising the total area produces a differential equation for r(s), which we don't need worry about now. However, we also have two boundary conditions for the left and right rings (with respective radii, a and b) spaced a total distance, d, apart,r(0) = a,r(d) = b.Without loss of generality, we can set a = 1; all lengths are measured in terms of the size of the right ring. For an unknown parameter, 0