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.

(In reply to Good going by Larry)

I have suggested an ellipse in the first comment.

I have constrained the square as my reference. 

It is clear that an ellipse being elongated will eventually result in a triangle, as described in my opening remark, being able to equate to in area of that of the square. I just need to determine the denominators of the elliptical equation and the coordinates of the base vertices of the triangle which will determine the ellipse.

Maybe this concept does not fit the definitions of 'range' and 'domain' but I'd be interested as to the values that make the three objects conform at least to the equal inscribed area within the bounds of a simple equation.

Posted by brianjn on 2007-06-13 08:55:37