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?

(In reply to re(2): Solution -- You're right; I'm wrong by McWorter)

To find t if a and b are given and we have

t^2 = a*b

Let a+b be the diameter of a circle. Construct a perpendicular to the diameter at the point that separates a and b. The distance from that point to the intersection of the perpendicular with the circle is the length t.

Posted by Bractals on 2005-08-17 00:31:26