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January 22nd, 2017, 05:01 PM   #1
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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.
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January 22nd, 2017, 09:43 PM   #2
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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
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Last edited by Maschke; January 22nd, 2017 at 09:48 PM.
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January 23rd, 2017, 12:37 PM   #3
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Quote:
Originally Posted by Maschke View Post
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
Oh that is really cool! Thanks for sharing that link!
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January 23rd, 2017, 12:55 PM   #4
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Don't start running in circles, Len !
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