PROBLEM OF THE MONTH

December 2006




Congratulations to Say Cheong, this month's winner! Here is his solution: [pdf]

Is there a polyhedron and a point outside of it, from which no vertex of the polyhedron is visible? The same question for a convex polyhedron? Justify your answers.

Recall that a polyhedron is a connected set obtained as a union of finitely many convex polyhedra. For example, if we remove a small cube from the interior of a bigger cube, then we obtain a (non-convex) polyhedron.

This month's prize will be awarded to the best explained, correct solution.


Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: January 1st at 12 pm.