Tom (and everyone else), sqrt(998) returns the value of 'sqrt(998)', whereas sqrt(1001) returns the value of '31.63858404', so the lookup table for square roots seems to be limited to 1000. As for how precise the results need to be, it is convinced by: ln(640320^3+744)/sqrt(163) but not by: sqrt(sqrt(9^2+19^2/22)) both of which, incidentally, were discovered by Ramanujan. Sincerely, Adam P. Goucher ----- Original Message ----- From: "Tom Rokicki" <rokicki@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Cc: "Henry Baker" <hbaker1@pipeline.com> Sent: Friday, May 06, 2011 7:00 PM Subject: Re: [math-fun] Symbolic Calculation
The expression:
ln(640320^3+744)/sqrt(163)
is an *approximation* for pi, accurate to 31 decimal places. As the calculator prints the symbol for pi when given this expression as input, it must be performing an inverse lookup.
I'm not sure this constitutes proof.
I'd love to get my hands on that calculator to see what sort of expressions it can reduce to symbols, and what it can't. And how accurate the result has to be.
I mean, certainly it doesn't have a lookup table that handles, for instance, sqrt(102305609)?
-tom
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