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 Comment by TomM)

Sorry about that. I hit "Enter" prematurely.

What I wanted to say was that we know it encloses the greatest area when it is a circle.

And can show that given certain constraints (Must be an n-gon, or must be a regular polygon, etc) that the more closely the enclosed space resembles a circle, the greater the area.

And we know that in nature, surface tension tends to pull a raindrop into a spherical shape, just as gravity pulls proto-planets into sheroids.

But just how easy is t to prove it?

Posted by TomM on 2002-06-03 12:51:05