(O.T.) Happy Pi Approximation Day! 'e*XROOT(12,e^(-3*4)+5.6789)' (N.T.) « Next Oldest | Next Newest »

 ▼ Gerson W. Barbosa Unregistered Posts: 2,761 Threads: 100 Joined: Jul 2005 07-22-2009, 05:04 PM ▼ Paul Dale Unregistered Posts: 3,229 Threads: 42 Joined: Jul 2006 07-22-2009, 05:32 PM Very nice. - Pauli ▼ Gerson W. Barbosa Unregistered Posts: 2,761 Threads: 100 Joined: Jul 2005 07-22-2009, 06:02 PM 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 Unregistered Posts: 283 Threads: 33 Joined: Jul 2008 07-22-2009, 06:37 PM Five seconds on a 48G gave me this: 1146408/364913 The old regular 22/7 is a bit easier to remember. Mark ▼ Paul Dale Unregistered Posts: 3,229 Threads: 42 Joined: Jul 2006 07-22-2009, 07:10 PM But neither of them use the digits 1 through 9 in order :-) - Pauli Gerson W. Barbosa Unregistered Posts: 2,761 Threads: 100 Joined: Jul 2005 07-22-2009, 07:25 PM 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. ▼ Thomas Radtke Unregistered Posts: 1,089 Threads: 32 Joined: Dec 2005 07-23-2009, 03:18 AM 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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