WP 34S calculates "almost integers" (fun result)
10-14-2014, 05:09 PM (This post was last modified: 10-14-2014 05:15 PM by Peter Van Roy.)
Post: #1
 Peter Van Roy Junior Member Posts: 21 Joined: Jan 2014
WP 34S calculates "almost integers" (fun result)
The WP 34S can calculate a famous "almost integer", exp(pi * sqrt(163)), which is sometimes called Ramanujan's number. In double precision mode (34 digits), a simple calculation returns:
Quote:262,537,412,640,768,743.9999999999992474
The actual answer (according to Wikipedia) is:
Quote:262,537,412,640,768,743.99999999999925007
No other handheld calculator in the world can do this, AFAIK.

Peter

PS: The Wikipedia entry gives exp(pi * sqrt(67)) as another almost integer, but I find that exp(pi * sqrt(58)) is of higher quality: it gives an error almost an order of magnitude smaller. Just a few minutes with my WP 34S to find the best "almost integers" of the form exp(pi * sqrt(n)).
10-14-2014, 06:13 PM
Post: #2
 DavidM Senior Member Posts: 835 Joined: Dec 2013
RE: WP 34S calculates "almost integers" (fun result)
(10-14-2014 05:09 PM)Peter Van Roy Wrote:  ...No other handheld calculator in the world can do this, AFAIK.

That may depend on your definition of "handheld calculator".

A 49g+/50g with the LongFloat library installed can also compute this value. Mine is currently set to 80 digits, and agrees with Wolfram Alpha's representation of this number for the first 78 of them.

Does that count?
10-14-2014, 06:26 PM
Post: #3
 Peter Van Roy Junior Member Posts: 21 Joined: Jan 2014
RE: WP 34S calculates "almost integers" (fun result)
(10-14-2014 06:13 PM)DavidM Wrote:
(10-14-2014 05:09 PM)Peter Van Roy Wrote:  ...No other handheld calculator in the world can do this, AFAIK.

That may depend on your definition of "handheld calculator".

A 49g+/50g with the LongFloat library installed can also compute this value. Mine is currently set to 80 digits, and agrees with Wolfram Alpha's representation of this number for the first 78 of them.

Does that count?

Out of the box your 49g+/50g can't do it. With proper libraries, many calculators can do it - any calculator with CAS can easily have the libraries added. But out of the box, they are not there.
10-14-2014, 07:47 PM
Post: #4
 DavidM Senior Member Posts: 835 Joined: Dec 2013
RE: WP 34S calculates "almost integers" (fun result)
(10-14-2014 06:26 PM)Peter Van Roy Wrote:  Out of the box your 49g+/50g can't do it. With proper libraries, many calculators can do it - any calculator with CAS can easily have the libraries added. But out of the box, they are not there.

I know this is just for fun, and I'm not trying to be argumentative. But from my perspective, a 34s is no more "out of box" than any other unit with customized software installed. Don't get me wrong -- I'm very respectful and appreciative of the 34s and what it can do in a package with no more memory than it has. It is truly a wonderful achievement, and I'm definitely a big fan.

If you change your original assertion to saying the 34s is the fastest (and easiest) handheld that can evaluate that expression to 31 digits, then I would have to agree with you.
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