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Article #61

Re: Pi day

#61
From: R.W.Dirksen
Date: Fri, 28 Mar 1997 00:00
49 lines
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Dik T. Winter wrote:
> 
> In article <5heh6s$ooa@raven.cc.ukans.edu> ipsifend@eagle.cc.ukans.edu (Greffindel) writes:
>  > So, it's pi x 1000 light-years, right?
>  > Speed of light: 3x10E8 m/s
>  > Seconds in a year: 60  x    60  x    24  x 365.25  =  31557600
>  >                 sec/min min/hour hour/day day/year
>  > m in a light-year: 9467280000000000 =9.46728 x 10E15 (I'm doing this
>  > all w/pencil and paper, so hit me if I biff the arithmetic).
>  > m in 1000 light-years: 9.46728 X 10E18
>  > Now, running a little c program on my home computer,
>  > 3.141592653589793239 is as much of pi as I can get without inventing
>  > my own quadruple=precision storage class, so let's see what that gives
>  > us:
> ...
>  > 2.852008848434121673571912 x 10E19, which in real numbers is
>  >  28520088484341216735.1912 meters.
>  > 18 decimal digits of pi gives you the distance correct down to the
>  > millimeter.  How much more pi do you need?
> 
> Are you sure?  I think the error in the speed of light and in the number
> of days in a year is much too large to warrant this assertion.
> 
> It is true, in real life 22/7 is mostly good enough, and if not you
> go to 355/133 which probably is excellent (it would be good enough
> in the calculation above).  On the other hand, there are indeed
> situations where you need an extremely good approximation of pi, or
> your calculations can go wrong.  There are highly unstable calculations
> (like some of the higher zeros of the Riemann zeta function) that
> require this.  (In the latter case to verify that all non-trivial zeros
> are on a particular line, you need to separate them.  The problem is
> that they can get arbitrarily close to each other.  And the calculations
> involve cosines.)
> --
> dik t. winter, cwi, kruislaan 413, 1098 sj  amsterdam, nederland, +31205924131
> home: bovenover 215, 1025 jn  amsterdam, nederland; http://www.cwi.nl/~dik/

The speed of light is known very exact because it is a constant value.
They actually made it a definition:

1 meter = the distance that light travels in 1/299792458 seconds
Therefore, the light speed c is defined as 299,792.458 km/s.

p.s. why celebrate pi-day anyway. I personally like the number
0.3157894736842105263157894736842105263157894736842105263157894736... 
or 6/19. That's why I celebrate that day instead!

Gerben Dirksen
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From: "R.W.Dirksen" <R.W.Dirksen@caiw.nl>
Subject: Re: Pi day
Date: 1997/03/28
Message-ID: <333C2695.5661@caiw.nl>
X-Deja-AN: 229108875
References: <AF5DA45C96685884D@sofluc.demon.co.uk> <ant262248d076Quo@cartmell.demon.co.uk> <5heh6s$ooa@raven.cc.ukans.edu> <E7qArI.1KD@cwi.nl>
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