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Approximation of pi based on sqrt(10)
09-07-2017, 02:44 PM (This post was last modified: 09-07-2017 02:45 PM by Namir.)
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Namir Offline
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Approximation of pi based on sqrt(10)
I was playing with my new NumWorks calculator (OK, OK, I bragging about having one in my possession :-) ) and decided to examine how close sqrt(10) is to pi and try to obtain a (reasonable) continuous fraction to calculate the difference between sqrt(10) and pi. I got the following

pi is approx = sqrt(10) - 1/(48 + 1/(2 + 1/(1 + 1/(9 + 1/2))))

let the RHS be p, I got

(p - pi)/pi * 1E9 = 110.26

Using the approximation of q=355/113 I get

(p - pi)/pi * 1E9 = 84.91

So my approximation, based on sqrt(10), is a bit less accurate than 355/113 but by not a whopping difference (ratio of errors is about 1.3)!

:-)

Namir
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Approximation of pi based on sqrt(10) - Namir - 09-07-2017 02:44 PM



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