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