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I'm a math tutor at a community college, and one of the students recently asked me why it is always true that a *regular* polygon (regular meaning equiangular and equilateral) has maximum area for any given perimeter. It makes perfect intuitive sense, but neither I nor any of the other tutors could figure out a rigorous method to prove it (the key word here being "rigorous").

The textbook skirted around the issue, and Google is turning up fuzzy results at best. Wikipedia states that it is fact, but only cites a book from 1979 that would be difficult to find.

eCookies for the most elegant proof (::) (::) (::) :)

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# Proving Area of n-sided Polygons Maximizes When they are Regular?

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