Stretching a string along a cylinder
Source:
November 3, 2010
geometry unsolvedgeometry
Problem Statement
A solid right circular cylinder with height and base-radius has a solid hemisphere of radius resting upon it. The center of the hemisphere is on the axis of the cylinder. Let be any point on the surface of the hemisphere and the point on the base circle of the cylinder that is furthest from (measuring along the surface of the combined solid). A string is stretched over the surface from to so as to be as short as possible. Show that if the string is not in a plane, the straight line when produced cuts the curved surface of the cylinder.