What is the maximum area that could be enclosed by a piece of string 132 cm long? What shape would that area take?

What is the minimum area that could be enclosed by the same string? What shape will it take?

(In reply to Solution by Half-Mad)

H-M

That's exactly what I meant when I said that we can "prove" it if we put extra constraints on the figure. In this case, you showed that a rectangle moves from the extreme of a line to the opposit extreme of a square. And since a square is the rectangle that most closely resmbles a circle, it has the greatest area.

Levik:

It is a simple matter to actually prove this, or the regular n-gon restraint with "easy" differential calculus, but I'm at a loss as to how to even set up the equations to prove the general case.

Posted by TomM on 2002-06-05 07:10:07