PI
Dave Corcoran
Does anyone know to how many places has PI been calculated?
Does anyone know if this task is still being persued?
--
David Corcoran -@@
uunet!aspect!dave ~
In a society where anything goes eventually everything will.
quod...@bunyip.enet.dec.com
IN excess of 33,000,000 places, as I recall, there are several different
algorithms that have been used. Most organizations that have been involved in
calulating pi, have given up through lack of interest and / or significant
return.
Send mail, if you want pointers to some of the more recent papers on
calculating pi. Actually, nothing significant has happened for a few years...
--
Peter Quodling Internet: quod...@blumon.enet.dec.com
Digital Equipment Corporation UUCP: ...!decwrl!blumon.enet!quodling
Nashua, NH. I disclaim everything!!!
Dan Bernstein
> In article <70...@aspect.UUCP>, da...@aspect.UUCP (Dave Corcoran) writes:
> > Does anyone know to how many places has PI been calculated?
> Actually, nothing significant has happened for a few years...
Actually, the Chudnovskys recently jumped into the pi game with a
Ramanujan-type formula, and beat Kanada in the race to 10^9 digits.
That's rather significant to anyone who knows anything about the field.
---Dan
Mike Tighe
>printf("Hello world\n");
>Does anyone know to how many places has PI been calculated?
201,326,000 places according to Yasumasa Kanada. This was published in the
Proceedings of Superocmputing 88.
--
-----------------------------------------------------------
Mike Tighe, Internet: ti...@convex.com
Voice: (214) 497-4206 Fax: (214) 497-4550
-----------------------------------------------------------
Scott Horne
<
The last figure I heard was 5,000,000 digits by a group in Japan.
<Does anyone know if this task is still being persued?
Of course it's still being pursued. The task of getting more and more digits
of pi has been pursued for thousands of years, with no sign of stopping.
What about memorising digits of pi? I know only about 400 digits. Any other
netters want to compete? :-)
--Scott
--
Scott Horne ...!{harvard,cmcl2,decvax}!yale!horne
ho...@cs.Yale.edu SnailMail: Box 7196 Yale Station, New Haven, CT 06520
203 436-1817 Residence: Rm 1817 Silliman College, Yale Univ
Uneasy lies the head that wears the _gao1 mao4zi_.
brpl...@miavx0.ham.muohio.edu
billion decimal places and it keeps going and going and ...
brian
{signature on strike}
brpl...@miavx0.ham.muohio.edu
mail would be great, but a post would be adeqate.
thanx
brian
{signature on strike}
60276000
OK, how about someone providing a method of calcing pi? i'm using
p=2
s=0
do
s=sqrt(s+2)
p=2*p/s
while (s < 2)
where p converges to pi as s converges to 2 but i'm interested in
any other algorhythms out there
John Eaton
< IN excess of 33,000,000 places, as I recall, there are several different
< algorithms that have been used. Most organizations that have been involved in
< calulating pi, have given up through lack of interest and / or significant
< return.
Nope, its Federal Law. Calculating Pi is a very dangerous operaton. What if
some researcher discovers that Pi repeats after 100,000,000,000 digits? The
universe as we know it would then cease to exist. Congress was made aware of
this and passed a law prohibiting the calculation of Pi past ten million
digits. The only organization authorized to conduct research in this area
is a special branch of the Armys Doomsday Machine research operation. They
have machines designed so even if one discovers the answer that it will not
tell anyone about it.
John Eaton
!hpvcfs1!johne
Al Dunbar
>In article <70...@aspect.UUCP> da...@aspect.UUCP (Dave Corcoran) writes:
>>printf("Hello world\n");
>
>>Does anyone know to how many places has PI been calculated?
>
>201,326,000 places according to Yasumasa Kanada. This was published in the
>Proceedings of Superocmputing 88.
places. Unfortunately, you don't get much desert that way :-)
-------------------+-------------------------------------------
Al Dunbar |
Edmonton, Alberta | "this mind left intentionally blank"
CANADA | - Manuel Writer
-------------------+-------------------------------------------
Ken Lerman
I usually get myself a square dartboard two feet on a side and
inscribe a circle with a radius of one foot. Then, by throwing darts
at the board and counting the ratio of darts which are inside the
circle to darts which hit the board, I can easily calculate pi.
Of course, this technique is only usable by those who are as bad at
darts as your average random number generator. :-)
Ken
Gary Strand
> DOES ANYONE HAVE AN ALGORITHEM TO CALCULATE PI TO THE NTH DECIMAL
Unless you've got a Cray and some very sophisticated algorithms, I don't
think you would get past the accuracy of your machine, in a timely fashion.
--
Gary Strand There is only one success -- to be able
Internet: stra...@ncar.ucar.edu to spend your life in your own way.
Voicenet: (303) 497-1336 - Christopher Morley
William K. McFadden
>In article <70...@aspect.UUCP> da...@aspect.UUCP (Dave Corcoran) writes:
>What about memorising digits of pi? I know only about 400 digits. Any other
>netters want to compete? :-)
I've only managed to remember 30 digits: 3.14159265358979323846264338327
(I hope I've remembered correctly :-)
I've never really needed more than 3 digits, though.
--
Bill McFadden Tektronix, Inc. P.O. Box 500 MS 58-639 Beaverton, OR 97077
bi...@videovax.tv.tek.com, {hplabs,uw-beaver,decvax}!tektronix!videovax!bill
Phone: (503) 627-6920 "The biggest difference between developing a missle
component and a toy is the 'cost constraint.'" -- John Anderson, Engineer, TI
Herman Rubin
> > "brian" (brpl...@miavx0.ham.muohio.edu)
> > DOES ANYONE HAVE AN ALGORITHEM TO CALCULATE PI TO THE NTH DECIMAL
> Unless you've got a Cray and some very sophisticated algorithms, I don't
> think you would get past the accuracy of your machine, in a timely fashion.
Not so, if you mean the "built-in" accuracy. Getting quite a few thousand
digits is no real problem. You do need good integer arithmetic algorithms.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hru...@l.cc.purdue.edu (Internet, bitnet) {purdue,pur-ee}!l.cc!hrubin(UUCP)
Gene Spafford
suggest the following book:
Pi and the AGM: A Study in Analytic Number Theory and Computational
Complexity
by Jonathan M. Borwein and Peter B. Borwein
Wiley-Interscience, 1987
ISBN 0-471-83138-7
The AGM in the article is the arithmetic-geometric mean iteration
method of Gauss, Lagrange and Legendre.
From the book:
First recorded attempt to calculate Pi was 2000 BC
As of July 1986 (just prior to publication) Kanada had calculated
2**25 decimal digits of Pi using an algorithm that is described in the book.
I assume his later results use a modification of the same algorithm.
--
Gene Spafford
NSF/Purdue/U of Florida Software Engineering Research Center,
Dept. of Computer Sciences, Purdue University, W. Lafayette IN 47907-2004
Internet: sp...@cs.purdue.edu uucp: ...!{decwrl,gatech,ucbvax}!purdue!spaf
Roy Smith
This may be a silly question, but other than "because it's there",
why have people spent so much time (and money) calculating PI?
--
Roy Smith, Public Health Research Institute
455 First Avenue, New York, NY 10016
r...@alanine.phri.nyu.edu -OR- {att,cmcl2,rutgers,hombre}!phri!roy
"Arcane? Did you say arcane? It wouldn't be Unix if it wasn't arcane!"
Richard Milward
355/113, which is accurate to about 10**-6.
See also _The Story of Pi_ (or is it _The Book of Pi_?)
(I'll post the real name, author, etc. tomorrow...)
--Richard Milward / network tech / UNC-CH / ODVC
Office of Data & Video Communications
"Your desires flow through our wires."
J Greely
(Richard Milward) writes:
>An interesting and simple approximation to pi is
>355/113, which is accurate to about 10**-6.
Useful if you need to keep everything in integers, but otherwise you
might as well just learn 3.141593. If you ever need more precision,
it'll be easier to extend that knowledge to get 3.1415926536 than it
will be to hunt up 312689/99532.
--
J Greely (jgr...@cis.ohio-state.edu; osu-cis!jgreely)
Roy Smith
> you might as well just learn 3.141593.
This may be silly, but I learned to memorise the first few digits
of PI in high school by the nice pattern they made on the keyboard of my
SR-10 calculator:
7 8 9
/
4 5 6
| / /
1 2 3
0 .
You have to remember the "3." youself, but after that, it's up from
the 1, then diagonal from the 1, then diagonal from the 2. On the other
hand, e doesn't make such a nice pattern (that I noticed), so as far as I
remember, e is just 2.something.
David J Bell
for PI, then said:
> On the other
>hand, e doesn't make such a nice pattern (that I noticed), so as far as I
>remember, e is just 2.something.
I dunno - the numeric pad pattern for e isn't that bad:
7 8 9
4 5 6
1 2 3
0
Now: e = 2.7182817, approximately.
2, diagonally to 7, drop to 1, diagonally to 8,
drop to 2, directly to 8, back to 1, and directly to 7.
You've just drawn the major diagonals and vertical edges of the
1-2-8-7 rectangle...
Dave db...@cup.portal.com
daniel lance herrick
>
>> DOES ANYONE HAVE AN ALGORITHEM TO CALCULATE PI TO THE NTH DECIMAL
>
> Unless you've got a Cray and some very sophisticated algorithms, I don't
> think you would get past the accuracy of your machine, in a timely fashion.
The multiple precision algorithms may be sophisticated, but they
are there in Knuth's The Art of Computer Programming.
You can find some interesting early work on the calculation of
large numbers by browsing through Scripta Mathematica from the
days of Jekuthiel Ginsberg's editorship. It carried reports of
work on rotary mechanical calculators generating the first 17
Mersenne numbers, for example. Someone helped that gentleman
calculate two numbers whose product is the 18th, or something
near it, on one of those electronic doodads.
I found Scripta Mathematica interesting recreational reading until
Ginsberg died. When his backlog was used up it became another
of those journals that carry papers that only ten people in the
world can read. The good issues are from the 1950s and early '60s.
dan herrick
herr...@iccgcc.decnet.ab.com
daniel lance herrick
> J Greely <jgr...@cis.ohio-state.edu> writes:
[clever mnemonic for pi omitted]
> On the other
> hand, e doesn't make such a nice pattern (that I noticed), so as far as I
> remember, e is just 2.something.
e is 2 . 1828 1828 45 90 45 ...
That's the part that has the simple mnemonic structure. You have to
memorize something to remember more.
As undergraduates, a couple of us computed e to 9845 decimals. That was
the amount that would fit twice into the 20000 digits of the IBM 1620
we did it on while leaving room for the add table and the program.
We told Professor Mielke what we had done and he showed us a nice fresh
paper in Mathematical Tables and Other Aids to Computation, by someone
at the David Taylor Model Basin (whose name I've been trying to remember
since this thread began) about the calculation of pi to 100,000 decimals.
A footnote offhandedly announced that they had also calculated e to the
same precision "by the obvious algorithm". I have a nice letter from
him and a reprint of the MTOC paper. And a listing of our results which
confirmed his first ten thousand places.
dan herrick
herr...@iccgcc.decnet.ab.com
daniel lance herrick
>
> e is 2 . 1828 1828 45 90 45 ...
>
> That's the part that has the simple mnemonic structure. You have to
> memorize something to remember more.
>
try
e is 2 . 7 1828 1828 45 90 45 ...
>
still, even with egg on my face,
> dan herrick
> herr...@iccgcc.decnet.ab.com
daniel lance herrick
How I wish I could recapture pi....
Eureka! cried the great inventor.
Christmas pudding, Christmas pie
Is at the problem's very center.
[Hint: number of letters in each word mean something.
]
Karl Heuer
> p=2; s=0; do s=sqrt(s+2); p=2*p/s; while (s < 2)
I use p=atan(1)*4, which gives me the answer in one iteration. :-) :-)
Karl W. Z. Heuer (ka...@ima.isc.com or uunet!ima!karl), The Walking Lint
Richard Milward
Ok, so I'm a day or 2 late...
The book I attempted to refer to is _A History of Pi_
by Petr Beckmann, St. Martin's Press, (c) 1971
Library of Congress catalog card no. 74-32539
(no ISBN number listed)
Chapter titles include: Euclid; Archimedes of Syracuse;
Newton; Euler; The Monte Carlo Method; and The Computer
Age. (A bit old, but fascinating.) A bibliography and
chronological table are included along with a listing
of the 1st 10,000 digits. A mention of the 1897 attempt
by the Indiana House of Representatives to legislate the
value of pi is also included.
Lots of approximation methods. No mnemonic aids.
(See _Scientific American_ May '82 p.32 in _Metamagical
Themas_ column for some of that.)
Joe Bob gives it a shrug -- I think it's okay :-)
--Richard Milward / UNC-CH / network tech
Almost forgot: using only 1-ohm resistors, how many will
it take, in any electrical network, to approximate pi
to within 10^^-6 ? I'll post some answers next week...
Scott Horne
<
<How I wish I could recapture pi....
<Eureka! cried the great inventor.
<Christmas pudding, Christmas pie
<Is at the problem's very center.
<
<[Hint: number of letters in each word mean something.
<]
The `at' doesn't belong. So much for that mnemonic. Oh, well, there are
many more where that came from. See Bergmann's book. I know a few that
even he doesn't list (though I don't use them myself).
The longest one I've seen is in Chinese. It's a poem (if you can call it that)
in which each character sounds like the corresponding digit in the decimal
expansion. (The decimal point is included.) Unfortunately, I don't remember
where I saw this. Could someone send me a reference? (A pointer to a Chinese
book is OK; I read Chinese.)
David J Bell
>Almost forgot: using only 1-ohm resistors, how many will
>it take, in any electrical network, to approximate pi
>to within 10^^-6 ? I'll post some answers next week...
Well, 40115 of the little devils would do it... Actually,
that would give accuracy to about 1 part in 10^8.
Sort of like the time a friend was bar hopping years ago, here
in Silicon Valley. He ran into this girl who worked in mark-and-pack
at the end of the assembly line at a local I.C. manufacturer. They
talked a while, maybe even on a coule of nights, and she told him
that she could "get him any I.C.s he wanted", right off the line.
Well, "Hell!" he says; why not. Tells her he could use whatever
7400s she could get. (Yeah this *was* a while back!) Couple weeks
later, he runs into her again and she says that she has something
in the car for him. Yep. About 2000 Seventy Four Zero Zeroes...
Now, isn't there a theorem that proves that you can build ANY logic
system, using only 2-input NAND gates?
Dave db...@cup.portal.com
(Oh yeah - spoiler:
Put 113 strings in parallel, each with 355 1 Ohm resistors...)
Timo Saarinen OH3YN
In article <2486.2...@iccgcc.decnet.ab.com> herr...@iccgcc.decnet.ab.com (daniel lance herrick) writes:
>When I admitted my gaffe here, someone passed this along to me:
>
>How I wish I could recapture pi....
>
>Eureka! cried the great inventor.
>
>Christmas pudding, Christmas pie
>
>Is at the problem's very center.
>
>[Hint: number of letters in each word mean something.
>]
One day, one friend of mine told me how to remember the value of pi
with fifteen digits:
How I need a drink. Alcoholic, of course - after the heavy chapters
describing quantum mechanics.
+--------------------------------------------------------------------------+
| - InterNet : ts7...@tut.fi | There's never enough time to do all |
| - HamRadio : OH...@OH3TR.FIN.EU | the nothing you want! (Calvin&Hobbes) |
+--------------------------------------------------------------------------+
Mark Harrison
From "The Lure of the Limerick":
'Tis a favorite value of mine,
A new value of PI to assign,
I would set it at three,
for it's simpler, you see,
Than three point one four five nine!
--
Mark Harrison harr...@necssd.NEC.COM
(214)518-5050 {necntc, cs.utexas.edu}!necssd!harrison
standard disclaimers apply...
Marshal L. Merriam
Scientific American, page 24, October 1985. The best was
How I wish I could enumerate pi easily,
since all these frigging mnemonics
prevent recalling any of pi's sequence
more simply.
(For those that haven't got it yet, the number of letters in each word
indicate the successive digits of $\pi$.)
I really enjoyed Petr Beckman's book "A History Of $\Pi$". (By the
way, my copy was copyright 1970,1971 by The Golem Press, ISBN: 0-911762-12-4,
LCCCN: 79-166154)
It does contain some of these poems (on page 105 in my copy,indexed under poems coding $\pi$)
in English, French, and German. Fortunately,
"The 32nd digit of $\Pi$ is zero, so that this kind of poetry
is mecifully nipped in the bud."
- Marshal L. Merriam
Scott Linn
How I wish I could recapture pi....
3. 1 4 1 5 9 2
Eureka! cried the great inventor.
6 5 3 5 8
Christmas pudding, Christmas pie
9 7 9 3
Is at the problem's very center.
2 2 3 8 4 6
^
Extra digit
>[Hint: number of letters in each word mean something.]
But, it's WRONG.
Scott Linn
Scott Horne
<
<Ok, so I'm a day or 2 late...
<The book I attempted to refer to is _A History of Pi_
<by Petr Beckmann, St. Martin's Press, (c) 1971
<Library of Congress catalog card no. 74-32539
<(no ISBN number listed)
It's pretty good, except for the anti-socialist propaganda....
<Lots of approximation methods. No mnemonic aids.
My copy (third edition) includes three or four mnemonic aids, including some
for French and German. And I wouldn't say that it contains "[l]ots of
approximation methods"; there are much better sources.
<Almost forgot: using only 1-ohm resistors, how many will
<it take, in any electrical network, to approximate pi
<to within 10^^-6 ? I'll post some answers next week...
One. Cut out a strip of paper of width twice the length of the resistor,
draw a line down the middle,.... :-)
Scott Horne
>In article <JGREELY.90...@morganucodon.cis.ohio-state.edu>,
<jgr...@morganucodon.cis.ohio-state.edu (J Greely) writes:
<< you might as well just learn 3.141593.
<
<From "The Lure of the Limerick":
<
< 'Tis a favorite value of mine,
< A new value of PI to assign,
< I would set it at three,
< for it's simpler, you see,
< Than three point one four five nine!
First, it's "three point one four ONE five nine" ("two six five three...").
Your knowledge of poetry, if not of pi, should've told you that.
Second, I hope no one mistakenly supposes that the lengths of the words in
that limerick represent the first few digits of pi. `[F]avorite' spoils it.
Third, setting it at three is a foolish idea which has been tried many times
throughout history. (Some have even tried to set it at four!)
Mark Harrison
> In article <5...@necssd.NEC.COM> harr...@necssd.NEC.COM (Mark Harrison) writes:
> < 'Tis a favorite value of mine,
> < A new value of PI to assign,
> < I would set it at three,
> < for it's simpler, you see,
> < Than three point one four five nine!
> First, it's "three point one four ONE five nine" ("two six five three...").
> Your knowledge of poetry, if not of pi, should've told you that.
I screwed up... yes, there should be a "one" there... also, in
checking the original, "value" in the first line should read
"project"... apologies to all...
> Third, setting it at three is a foolish idea which has been tried many times
> throughout history. (Some have even tried to set it at four!)
It's a joke. Please DO NOT take it seriously.
Special to Scott: I *like* the anti-socialist propoganda in
"A History of Pi". :-)
Anders Thulin
>
>How I wish I could recapture pi....
>Eureka! cried the great inventor.
>Christmas pudding, Christmas pie
>Is at the problem's very center.
Ludolph van Ceulen spent much time calculating pi to 35 (?) decimal places.
He also wrote a verse (in Latin) for remembering the first 32.
Unfortunately I have forgotten how it went ... :-)
--
Anders Thulin a...@prosys.se {uunet,mcsun}!sunic!prosys!ath
Telesoft Europe AB, Teknikringen 2B, S-583 30 Linkoping, Sweden
Mike Carvin
>In article <95...@ncar.ucar.edu>, ga...@ncar.ucar.EDU (Gary Strand) writes:
>>> "brian" (brpl...@miavx0.ham.muohio.edu)
>>
>>> DOES ANYONE HAVE AN ALGORITHEM TO CALCULATE PI TO THE NTH DECIMAL
>>
I kinda like the following myself:
How I need a drink! Alcoholic, of course, after all
night studying quantum mechanics!
Counting the letters in each word, you get:
3.1415926535879
--
========================================================================
Mike Carvin | m...@world.std.com
| car...@sud509.ed.ray.com
========================================================================