Isoperimetric Theorem what does it mean

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ultrabionic_ang
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so i was reading something on the isoperimetric theorem at this link:http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml"

and I'm having a difficult time trying to understand it, much less put the theorem into my own words.
 
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If you were designing a fence to enclose a certain set area, what shape would you create with the fence so that you use the least amount of fencing material ? The theorem states that the circle is that shape.