Fun_People Archive
17 Oct
FUN with PI

Content-Type: text/plain
Mime-Version: 1.0 (NeXT Mail 3.3 v118.2)
From: Peter Langston <psl>
Date: Thu, 17 Oct 96 00:17:08 -0700
To: Fun_People
Subject: FUN with PI

Forwarded-by: Neil Gershenfeld <neilg@media.mit.edu>
From: Barrie Gilbert <Barrie.Gilbert@analog.com>


I once wrote a piece about pi distinguished
by its typographically circular form. Alas,
it has disappeared somewhere in cyberspace,
or possibly it's joined the lost luggage in
the dusty rings of Saturn. Anyway, during a
lengthy simulation today, I thought I'd try
again. This time, instead of just one large
circle, I thought it would be much more fun
to put this brief story into "three and one
seventh" circles. (The "one seventh" wasn't
so easy). Further, it shares pi's character
in not finishing in a satisfying manner. If
this brings a wry smile to your face, it'll
have fully served its Saturday mission. The
question remains, what IS the next rational
fraction that evaluates to pi with a higher
accuracy than 85          parts per billion
which is the                   error in 355
over 113?                         BG knows!

                    __
                  Pi, that
              most wonderfully
           enigmatic ratio of the
         circumference of a circle
        to its diameter, was already
       familiar to writers of a Bible
       text, who speak about a copper
      basin used for ritual cleansings
      in the Second Book of Chronicles
      chapter four verse two, as being
      thirty cubits in compass and ten
       cubits from brim to brim. This
       isn't quite precise enough for
         modern use. But, who needs
           computers, calculators
              or similar kinds
                  of tools
                     --
                     __
                  in order
              to fathom such a
           deep matter to endless
         decimal places? If three's
        close enough for God, who am
       I to question his mathematical
       genius? A North Carolina court
      many years ago deliberated a law
      that required Pi to have a value
      of three in schools and business
      matters. Such a curious proposal
       reflected the misunderstanding
       of the people of the time. The
        popular approximation for Pi
         is 22/7, and this is close
           enough for most of our
              needs arising in
                  numerous
                     --
                     __
                  everyday
              situations. When
           you need a little more
         accuracy, you ought to try
        the ratio 355/113 - which is
       noteworthy not only because of
       its remarkable accuracy, being
      only 85 parts per billion higher
      that the definitive value; it is
      also composed of the first three
      prime numbers, each one occuring
       twice. Note also that, just as
       for the 22/7 approximation the
        numerator is NOT prime while
         the denominator is. Do you
           know the next rational
              approximation of
                  Pi? That
                     --
                     __
                  is, next
              in sequence that
           produces a lower error

© 1996 Peter Langston