Perhaps I should define my terms. The solid angle at a point on a convex surface S is the limit of the solid angle subtended by the surface in an epsilon-neighborhood N(eps) of the point, as epsilon -> 0. And that is the area on the unit sphere of the set of all perpendicular unit vectors to the supporting hyperplanes* to S on N(eps) (when the vectors are translated to the origin). --Dan ________________________________________________________ * < http://en.wikipedia.org/wiki/Supporting_hyperplane >
On Feb 2, 2015, at 10:27 AM, Daniel Asimov <asimov@msri.org> wrote:
Consider the tricylinder T -- the intersection of three cylinders each of unit radius in 3-space with perpendicular axes. Let S denote its surface bd(T).
PUZZLE: Find the solid angle in closed form at a point of S common to the 3 cylinders.
--Dan