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January 22nd, 2017, 05:01 PM  #1 
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  EASY Way to Find the Area of a Circle
I just thought of a quick simple way to find the area of a circle. Imagine a circle by which it's radius is expanding. At any point you can define the length of it's circumference by multiplying 2*radius*PI. Well then, 2PIr is simply the rate by which our circle is increasing in area with respect to the increasing radius. Integrate 2PIr PIr^2 I am quite sure many people have already thought of it though being as simple as it is. 
January 22nd, 2017, 09:43 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,571 Thanks: 379 
Here's a discussion of that observation. It works for spheres of arbitrary dimension. There are a number of interesting points of view and additional web references. calculus  Why is the derivative of a circle's area its perimeter (and similarly for spheres)?  Mathematics Stack Exchange Last edited by Maschke; January 22nd, 2017 at 09:48 PM. 
January 23rd, 2017, 12:37 PM  #3  
Senior Member Joined: Jul 2016 From: USA Posts: 108 Thanks: 13  Quote:
 
January 23rd, 2017, 12:55 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,688 Thanks: 701 
Don't start running in circles, Len !


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area, circle, easy, find 
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