🚀 go-pugleaf

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/