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.

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TopNewestThis result is known as the Isoperimetric Theorem: http://en.wikipedia.org/wiki/Isoperimetric_inequality. – Jon Haussmann · 2 years, 1 month ago

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– Calvin Lin Staff · 2 years, 1 month 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?Log in to reply

– Jon Haussmann · 2 years, 1 month ago

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

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. – Nihar Mahajan · 2 years, 1 month agoLog in to reply