# Is this well known?

I feel that this problem has been solved, but am unable to find a solution to it:

Given a string of fixed length, how should it be bent so that the area it encloses is maximal?

I believe that the solution is folding it into a circle, but am unsure whether it has been proven.

Note by Alex Li
3 years ago

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This result is known as the Isoperimetric Theorem: http://en.wikipedia.org/wiki/Isoperimetric_inequality.

- 3 years ago

I am often hardpressed for an actual proof of it. WIkipedia says "Since then, many other proofs have been found, some of them stunningly simple.", do you have any ideas on how it can be shown?

Staff - 3 years ago

I once saw a proof in a differential geometry class. I do not know of any simple proofs.

- 3 years ago

I think the question must ask for maximum.If it asks for minimum , then the area is 0 since we can just overlap the thread.

Edit: The problem poster edited the problem.

- 3 years ago