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.

The degree zero equation y=a with domain restriction from 0 to 2a creates a rectangle twice as wide as it is high.

The largest square is a*a = a^2

The largest triangle is .5*a*2a = a^2

I'm not sure if this violates what is meant by "inscribed" though.

 

Posted by Jer on 2007-06-12 11:46:03