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.

#Geometry #Area #Perimeter #Circle #Circles

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Comments

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

Jon Haussmann - 6 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?

Calvin Lin Staff - 6 years ago

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

Jon Haussmann - 6 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.

Nihar Mahajan - 6 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$