January 31st, 2015, 01:29 AM  #1 
Newbie Joined: Aug 2012 Posts: 22 Thanks: 0  Perimeter and area of the circle
How to prove that a circle has the maximum possible area for a given perimeter, and the minimum possible perimeter for a given area.

January 31st, 2015, 05:17 AM  #2  
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra 
This is the so called isoperimetric problem. Quote:
 
January 31st, 2015, 06:06 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
A general proof would require "Calculus of Variations" Calculus of Variations  from Wolfram MathWorld. Are you familiar with that?

January 31st, 2015, 06:39 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,888 Thanks: 1836 
See .


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