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+--- Thread: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) (/thread-153373.html)
(O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Gerson W. Barbosa - 07-22-2009
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Paul Dale - 07-22-2009
Very nice.
- Pauli
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Gerson W. Barbosa - 07-22-2009
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.
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Mark Edmonds - 07-22-2009
Five seconds on a 48G gave me this: 1146408/364913
The old regular 22/7 is a bit easier to remember.
Mark
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Paul Dale - 07-22-2009
But neither of them use the digits 1 through 9 in order :-)
- Pauli
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Gerson W. Barbosa - 07-22-2009
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.
-------
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.
Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) - Thomas Radtke - 07-23-2009
Quote:HP-35 users knew that one before (mentioned in its manual) ;^).
P. S.: The 33s gives instantly this even better and still easy to remember approximation:-)
355
Pi ~ ---
113