While buttering my bread at lunch one day I mused that one can not only cut a square pat of butter in half with only a knife, but also if the pat is in the shape of a regular n-gon, n>3. But what if the pat is shaped like an irregular quadrilateral?

Can you bisect the area of an arbitrary quadrilateral with one straight line using only a straightedge and a compass?

It is implied that the pat of butter has a uniform thickness, otherwise halving the face would not necessarily halve the pat. This implies that the sides of the pat are rectangles. I would turn the pat of butter up on one of its sides and slice along the midpoints of the opposite "height" sides of the upturned rectangular face.

Edited on August 17, 2005, 11:48 am

Posted by owl on 2005-08-17 03:10:06