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To Max and Seva

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Post by Rishi Wed Apr 17, 2013 8:55 am

I am just curious whether you know how to show 22/7 > pi by using integration of an expression limits 0 to 1?

Rishi

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Post by Rishi Wed Apr 17, 2013 9:38 am

I take it back.

Wikipedia says this is a question on the IIT JEE.

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Post by Seva Lamberdar Wed Apr 17, 2013 10:11 am

If you can come up with an expression e.g. for circumference of a circle (c = total circumference / 4) in terms of the x coordinate, c = c(x) , then you can integrate that expression with respect to x ( 0 --> 1). The resulting numerical value for c (through integration) will correspond to the actual value of pi/2, since the total circumference = 4c = 2*pi (@x=1).
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https://docs.google.com/document/d/1bYp0igbxHcmg1G1J-qw0VUBSn7Fu

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Post by MaxEntropy_Man Wed Apr 17, 2013 8:04 pm

is this what you were looking for:

http://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80

i didn't know this.
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