## Files are just approximations of Pi...

All those files in your computer. What are they exactly? Well,
they are just approximations of that wonderful number,
. Some are
good, some are bad, but each file is an approximation. What did
I smoke? Nothing... Let me explain.

It is well known that the probability of two integers being coprime is
6/^{2}. It can even be proved.

Now, if a file is structured as a list of lines, each line can be
seen as a number (a field of bits being a number in base
two). Considering the probability for each line to be coprime with the
next line, any file provides an approximation of .
All you have to do to obtain the approximation for a given file is
to compute the `gcd`

of quite large numbers.

Here is a Perl script that
computes the number of a given file.

Of course, the larger and the more random a file is, the better
the approximation. For instance, the number of my
Ph.D. thesis (uuencoded Postscript) is 3.302 (but I am currently
writing a research paper with a number (at present) equal to 42.001).

The kernel of windoze 98 gives the outstanding approximation of
3.14159265358979323846264338327950. This proves that this program is
**NOT** randomly generated (as many people seem to
believe). With a pseudo random (`rand48`

) 10 GB/41943040 lines
file (and an optimized `C/gmp`

program to compute the
number instead of the Perl script), I only got 3.141543785 (and a $1,000 fine from Caltech for wasting
56 hours of CPU time...).

The current
record (00/02/18) in the computation of is
206,158,430,000 digits. What
is funny, is that it only took 37 hours and 21 minutes. However, I
don't know what random file they used...

So, what's the best file on your machine?

Michel Charpentier <>
Last modified: Wed Nov 29 08:45:02 EST 2000