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From: kremen@aero.ARPA (Gary Kremen)
Newsgroups: net.micro,net.math
Subject: RE: PI - not apple
Message-ID: <174@aero.ARPA>
Date: Mon, 30-Dec-85 18:11:12 EST
Article-I.D.: aero.174
Posted: Mon Dec 30 18:11:12 1985
Date-Received: Wed, 1-Jan-86 00:48:44 EST
References: Upon request
Reply-To: kremen@aero.UUCP (Gary Kremen)
Organization: The Aerospace Corporation, El Segundo, CA
Lines: 35
Xref: watmath net.micro:13326 net.math:2649

Some comments on computation of PI

1) There was a recent posting on the exactness of pi/4 = 4*atan(1/5) -
atan(1/239). This is a true relationship. You can easily prove this by
taking the tangents of both sides and using the tan(a+b) relationship.

2) Sheldon Meth talked about the simplicity of using the expansion of
atan(1) which is equal to pi/4. Yes, it is simple but it converges
extremely slow.

3) There is a new method of calculating PI discovered in 1976. It is
asymetrically faster than using arctan methods. It is pretty complex. If
there is any interest I will post info to the net.

4) In 1983 I computed PI to 225,000 digits using IBM 4341. No problem,
but it took 1.1 days of machine time. It was lucky I was the machine's
only operator. I wrote the program in very optimized FORTRAN/assembly
code.  Recently I rewrote it in C, for use on microcomputers.

5) There is a book "A History of Pi" by Peter Beckmann. It is well worth
reading even if you don't have a mathematics background. He explains how
history of progress in Pi and mathematics mirrors man's history. For
example - during the dark ages the most enlighted countries have the
most mathematics progress.

6) Current Pi record is around 16 million places.
--
Name: Gary Kremen
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