Problem Contest – Problem of the Week – March 16, 2004

Geometry of a Convex Set: Let S be a convex set in the real plane (that is, if p and q are in S then the line segment pq is contained in S). Do there always exist two perpendicular lines that divide the area of S into four equal pieces?  Prove or give a counterexample.

[Problem contributed by Professor Bruce Peterson}

Submit written solution with justification to John Emerson, Warner 312, before 3:00 on Tuesday, March 30.  Or leave them in the Warner mailroom.

Note:  Join us at the weekly seminars, usually on Tuesday at 3:00 for refreshments.