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 ngon, 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 20050817 00:31:26 