kremen@aero.ARPA (Gary Kremen) (12/31/85)
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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Disclaimer 1: "The company does not know what I am doing"
Disclaimer 2: "Both the company and I have great lawyers"percus@acf4.UUCP (Allon G. Percus) (01/01/86)
> 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. However, if you have a history background, you'll love this book. In his explanations of Pi, his relations of history are superb and accurate. It's one of the best history books I've ever read. . ------- |-----| A. G. Percus |II II| (ARPA) percus@acf4 |II II| (NYU) percus.acf4 |II II| (UUCP) ...{allegra!ihnp4!seismo}!cmcl2!acf4!percus |II II| -------