The Museum of HP Calculators

HP Forum Archive 19

 (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.)Message #1 Posted by Gerson W. Barbosa on 22 July 2009, 5:04 p.m.

 Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.)Message #2 Posted by Paul Dale on 22 July 2009, 5:32 p.m.,in response to message #1 by Gerson W. Barbosa Very nice. - Pauli

 Re: (O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.)Message #3 Posted by Gerson W. Barbosa on 22 July 2009, 6:02 p.m.,in response to message #2 by Paul Dale 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.)Message #4 Posted by Mark Edmonds on 22 July 2009, 6:37 p.m.,in response to message #3 by Gerson W. Barbosa 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.)Message #5 Posted by Paul Dale on 22 July 2009, 7:10 p.m.,in response to message #4 by Mark Edmonds 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.)Message #6 Posted by Gerson W. Barbosa on 22 July 2009, 7:25 p.m.,in response to message #4 by Mark Edmonds 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: 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.)Message #7 Posted by Thomas Radtke on 23 July 2009, 3:18 a.m.,in response to message #6 by Gerson W. Barbosa 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) ;^).

Go back to the main exhibit hall