Approximation of pi based on sqrt(10)

[Dieter]

(09-07-2017 09:18 PM)Namir Wrote:  I was using the new NumWorks calculator. I am not surprised about the difference in the results you obtained.

The result for 355/113 is fine. But do you want to say that the relative error of the √10 approximation is returned as 1,1026 E–7 ?

You said:

Quote:let the RHS be p, I got
(p - pi)/pi * 1E9 = 110.26

Here p = √10 – 61/2949 = 3,141592682209749. Does the NumWorks calculator return a different value?

Pi = 3,141592653589793, and I assume that this is also true for the NumWorks calculator.

So (p – pi)/pi * 1E9 = 2,8619956E-8 / 3,141592653589793 * 1E9 = 9,1100149...

I cannot imagine that the NumWorks calculator really returns 110,26 for this.

On the other hand the relative error you mentioned (110,26 E–9) is returned if you assume that p = 3,141593 exactly instead of 3,14159268... May this be the reason for the result you got? Did you possibly do the calculation with p rounded to six decimal places?

Dieter