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



#8


#9

Very nice.

- Pauli


#10

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.


#11

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

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

Mark


#12

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

- Pauli

#13

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.


#14

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

      355
Pi ~ ---
113


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

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