Yet another new pi approximation
01-14-2017, 05:57 PM
Post: #1
 Gerson W. Barbosa Senior Member Posts: 1,419 Joined: Dec 2013
Yet another new pi approximation

$$e+\frac{69-e^{-2^{2}\ln \ln \left ( e^{e^{2}}+\ln \ln \left ( 2 \right ) \right )}}{163}$$

'e+(69-e^(-2^2*LN(LN(e^e^2+LN(LN(2))))))/163'
01-14-2017, 08:27 PM
Post: #2
 Maximilian Hohmann Senior Member Posts: 903 Joined: Dec 2013
RE: Yet another new pi approximation
I don't know... expressing one number with inifinite digits using another one? AFAIK, Euler once found a much more elegant way of linking Pi with e.
01-14-2017, 10:48 PM (This post was last modified: 01-22-2017 07:14 PM by Gerson W. Barbosa.)
Post: #3
 Gerson W. Barbosa Senior Member Posts: 1,419 Joined: Dec 2013
RE: Yet another new pi approximation
(01-14-2017 08:27 PM)Maximilian Hohmann Wrote:  I don't know... expressing one number with infinite digits using another one? AFAIK, Euler once found a much more elegant way of linking Pi with e.

This is just an approximation starting from the fact that 163∙(π - e) ≃ 69, not an exact relationship in the realm of complex numbers like Euler's beautiful and wonderful formula. I think my correction term involving two levels of exponentiation and logarithm and the integer number 2 may have some aesthetic value, anyway beauty lies in the eyes of the beholder :-)

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Edited (22:Jan)

The following doesn't require a wider HP-50g screen to show the whole equation...

...but it does require a 16-digit calculator to show the accuracy of approximation.

'e+(69-e^(-8/(1+1/(163*401))))/163'
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