(O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.)

[Gerson W. Barbosa]

[Paul Dale]

Very nice.

- Pauli

[Gerson W. Barbosa]

Thanks!

It took me only five minutes or so to find this one on the 12C:

3.141592654

ENTER

1 e^x /

ENTER ENTER ENTER

; now press * n times until something interesting shows on the display:

*  => 1.335705708  not close enough to sqrt(sqrt(pi)) -> ignore

*  => 1.543711618  don't recognize -> ignore

*  => 1.784109737  not close enough to sqrt(pi) -> ignore

*     and so on...

*

*

*  => 3.183047554  From memory, close to 10/pi -> near idendity (pi/e)^8 ~ 10/pi, but useless for my purpose

*

*

*

*  => 5.678906136 -> =(pi/e)^12. Since I have 12 and 56789, decide to try a pandigital approximation (only 3 and 4 missing).

                      Luckily e^-12 = e^(-3*4) does the job nicely! :-)

Gerson.

[Mark Edmonds]

Five seconds on a 48G gave me this: 1146408/364913

The old regular 22/7 is a bit easier to remember.

Mark

[Paul Dale]

But neither of them use the digits 1 through 9 in order :-)

- Pauli

[Gerson W. Barbosa]

Archimedes' upper bound for Pi is better because it was obtained by reasoning rather than sheer luck.

MathWord has plenty of Pi approximations to choose from:

http://mathworld.wolfram.com/PiApproximations.html

Regards,

Gerson.

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P. S.: The 33s gives instantly this even better and still easy to remember approximation:-)

      355

Pi ~  ---

      113

Edited: 22 July 2009, 7:35 p.m.

[Thomas Radtke]

Quote:

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P. S.: The 33s gives instantly this even better and still easy to remember approximation:-)

      355

Pi ~  ---

      113

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HP-35 users knew that one before (mentioned in its manual) ;^).