Approximation of pi based on sqrt(10)

[Namir]

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