Question 12
A polygon in the plane (with no self-intersections) is called equitable if every line passing through the origin divides the polygon into two (possibly disconnected) regions of equal area.
Does there exist an equitable polygon which is not centrally symmetric about the origin?
(A polygon is centrally symmetric about the origin if a 180-degree rotation about the origin sends the polygon to itself.)
Does there exist an equitable polygon which is not centrally symmetric about the origin?
(A polygon is centrally symmetric about the origin if a 180-degree rotation about the origin sends the polygon to itself.)