🚀 go-pugleaf

John Cartmell (john@cartmell.demon.co.uk) wrote:
: In article <AF5DA45C96685884D@sofluc.demon.co.uk>, Jonathan Cunningham
: <URL:mailto:jlc@sofluc.demon.co.uk> wrote:
: > 
: > In article <5gmqsn$bs8@milo.vcn.bc.ca>,
: > mgibson@vcn.bc.ca (Mark Gibson) wrote:
: > 
: > >Martin Ward (martin@ward-hull.demon.co.uk) wrote:
: > >: Pi day
: > >: 
: > (snip)
: > >
: > >3.14159265379 is a closer approximation to pi that I usually use. But that
: > 
: > Since I haven't seen anyone else say it yet, if you are going to use a 12
: > digit approximation, how about using 3.14159265359 which is an even better
: > approximation than the one you use :-).
: > 
: > I find "3" is accurate enough for many purposes, though.

: Quite true.  Making sausage rolls the pastry needs to be three widths
: of sausage and a bit.  The hardest thing to teach is when an
: approximation is appropriate.

(Feel free to shoot me down if I've got a detail slightly bobbled, but...)
I read once (and subsequently verified) that with 3.1415927 as an
approximation for pi, you can compute the circumference of the earth
(or rather, a perfect sphere having the same diameter as the earth)
and be off by only 6 or 7 inches... So it really begs the question--
when, if ever, are we likely to need more than 10 digits of pi?  

For the sake of argument, consider space travel.  Here's a rather
stupid story problem on the astronomical scale:  The obscure star
Smurfulus Eta is 1000 light-years from the centre of the galaxy.  As
the galaxy makes one full rotation about its own axis, how far does it
travel?  (Circular orbit, by the way.)

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:


(much later)

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?

: -- 
:      _/_/_/     _/          John Cartmell
:       _/ __/_/ _/_/  _/_/  using Acorn Risc PCs - and StrongARMed
:   _/ _/ _/ _/ _/ _/ _/ _/ UK designed and made - British software
:   _/_/ _/__/ _/ _/ _/ _/ supporting our own; even if it is the best ;-)


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