Find a shape for which the area of the largest inscribed triangle is equal to the area of the largest inscribed square.

No doubt there are an infinity of such shapes, but you must find one that can be expressed by a simple equation of order 2 or less, combined with constraints on the domain and range.

How about the interior of the unit circle
intersected with the first quadrant. The
square has one vertex at the origin, sides
aligned with the x an y axes, and the 
opposite vertex on the circle. The triangle
is an isosceles right triangle with the right
angle vertex at the origin, the legs aligned
with the x an y axes, and the other two
vertices on the circle. The area of the square
and the triangle is 1/2.

Posted by Bractals on 2007-06-12 13:19:27