# Fun_People Archive 17 OctFUN with PI

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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
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