From: jk87377@cc.tut.fi (Juhana Kouhia)
Subject: Re: Looking for fast methods of computing PI
Organization: Tampere University of Technology
Date: Tue, 13 Oct 92 12:48:15 GMT


In article <1992Oct13.025820.4593@eecs.nwu.edu> kaufman@eecs.nwu.edu
(Michael L. Kaufman) writes:
>
>I read an article a few years ago in some magazine (I think it was Discover)
>that talked about two people who had come up with a fast way of computing PI.

Hi,

The below is my updated list of pi references; there's some
interesting articles, for example:

  J.M. Borwein and P.B. Borwein
  More Ramanujan-type series for 1/pi
  pp. 359-374 in Ramanujan Revisited  [Proceedings of the 1987
  Illinois Ramanujan Centenary Conference], Academic Press(1988)
  -includes the series the Chudnovskys used in their record
   computation and many others of a similar ilk

Chudnovskys were the two people, I guess.
The proceeding is maybe difficult to find.

There is an article on them in New Yorker, but I don't have a
reference for it -- I supposed to be, but...  ok, I would like to get
the reference.
Also, if there's an article on Discover, then please...

Check article
  J.M. Borwein and P.B. Borwein
  Ramanujan and pi
  Scientific American, Feb 1988, pp. 112-117
for the start.


Juhana Kouhia


==============================================================================

Pi-references
-------------
Compiled by Juhana Kouhia, jk87377@cs.tut.fi
Last update Oct 13, 1992

Please send updates to Juhana Kouhia

Comments starting with '-' are written by J.M. Borwein
and Mark Brader (marked).

There's two electronic news articles written by Allan Adler and Mark
Brader about the law in the US state of Indiana which would have
assigned a value to pi, in the year 1897.
To get electronic news articles above, send a request to me.
[See also Edington and Singmaster references]

------------------------------------------------------------------------------

David H. Bailey
The computation of pi to 29,360,000 decimal digits using Borwein'
quartically convergent algorithm
Mathematics of Computation, Vol. 50, No. 181, Jan 1988, pp. 283-296

David H. Bailey
Numerical results on the transcendence of constants involving pi,
e, and Euler's constant
Mathematics of Computation, Vol. 50, No. 181, Jan 1988, pp. 275-281

P. Beckmann
A history of pi
Golem Press, CO, 1971 (fourth edition 1977)

J.M. Borwein and P.B. Borwein
The arithmetic-geometric mean and fast computation of elementary
functions
SIAM Review, Vol. 26, 1984, pp. 351-366

J.M. Borwein and P.B. Borwein
More quadratically converging algorithms for pi
Mathematics of Computation, Vol. 46, 1986, pp. 247-253

J.M. Borwein and P.B. Borwein
An explicit cubic iteration for 9
BIT, Vol. 26, 1986, pp. 123-126

J.M. Borwein and P.B. Borwein
Pi and the AGM. A Study in Analytic Number Theory and Computational Complexity
John Wiley & Sons. New York, 1987

J.M. Borwein and P.B. Borwein
More Ramanujan-type series for 1/pi
pp. 359-374 in Ramanujan Revisited  [Proceedings of the 1987
Illinois Ramanujan Centenary Conference], Academic Press(1988)
-includes the series the Chudnovskys used in their record
 computation and many others of a similar ilk

J.M. Borwein and P.B. Borwein
Ramanujan and pi
Scientific American, Feb 1988, pp. 112-117

J.M. Borwein, P.B. Borwein, and K. Dilcher
Euler numbers, asymptotic expansions and pi
American Mathematical Monthly, Vol. 96, 1989, pp. 681-687
-relates Gregory's series and Pi and Euler numbers

J.M. Borwein, P.B. Borwein, and D. A. Bailey
Ramanujan, modular equations and pi or how to compute a billion digits
of pi
American Mathematical Monthly, Vol. 96, 1989, pp. 201-219

J.M. Borwein and P.B. Borwein
Approximating pi with Ramanujan's solvable modular equations
Proceedings of the 1986 Edmonton conference on Constructive Function
Theory, Rocky Mountain J., Vol. 19, 1989, pp. 93-102
-gives the algebraically most surprising iterations for Pi

J.M. Borwein and P.B. Borwein
A cubic counterpart of Jacobi's identity and the AGM
Trans. Amer. Math. Soc., Vol. 323, 1991, pp. 691-701
-contains three of the fastest known iterations for Pi

J.M. Borwein and P.B. Borwein
Class number three Ramanujan type series for 1/pi
Journal of Computational and Applied Math (Special Issue), xx(1992)

J.M. Borwein and I.J.  Zucker
Elliptic integral evaluation of the Gamma function at rational values
of small denominator
IMA J. of Numer Analysis, xx(1992)
-includes agm based iterations for Gamma(n/24): since
 Gamma(1/2)=Pi^(1/2) this is closely related

Shlomo Breuer and Gideon Zwas
Mathematical-educational aspects of the computation of pi
Int. J. Math. Educ. Sci. Technol., Vol. 15, No. 2, 1984, pp. 231-244

Will E. Edington
House Bill No. 246, Indiana State Legislature, 1897
Proceedings of the Indiana Academy of Science, (month unknown), 1935
-This article is about the law in the US state of Indiana which would
 have assigned a value to pi, in the year 1897. [ -- Mark Brader]
[See also Singmaster article]

Harley Flanders
Algorithm of the bi-month: Computing pi
College Mathematics Journal, Vol. 18, 1987, pp. 230-235

Y. Kanada and Y. Tamura
Calculation of pi to 10,013,395 decimal places based on the
Gauss-Legendre algorithm and Gauss arctangent relation
Computer Centre, University of Tokyo, 1983

R. Lynch and H.A. Mavromatis
N-dimensional harmonic oscillator yields monotonic series for the
mathematical constant pi
Journal of Computational and Applied Mathematics, Vol. 30, No. 2,
May 1990,  pp. 127-137

H.A. Mavromatis
Two doubly infinite sets of series for pi
Journal of Approximation Theory, Vol. 60, 1990, pp. 1-10

N.D. Mermin
Pi in the sky
Letter to the Editor
American Journal of Physics, Vol. 55, 1987, p. 584

D.J. Newman
A simplified version of the fast algorithms of Brent and Salamin
Mathematics of Computation, Vol. 44, No. 169, Jan 1985, pp. 207-210

Morris Newman and Daniel Shanks
On a sequence arising in series for pi
Mathematics of computation, Vol. 42, No. 165, Jan 1984, pp. 199-217

E. Salamin
Computation of pi using arithmetic-geometric mean
Mathematics of Computation, Vol. 30, 1976, pp. 565-570

D. Shanks and J.W. Wrench, Jr.
Calculation of pi to 100,000 decimals
Mathematics of Computation, Vol. 16, 1962, pp. 76-99

Daniel Shanks
Dihedral quartic approximations and series for pi
J. Number Theory, Vol. 14, 1982, pp.397-423

David Singmaster
The legal values of pi
The Mathematical Intelligencer, Vol. 7, No. 2, 1985
[See also Edington article]

John Todd
A very large slice of pi
Review for the book "Pi and the AGM. A study in analytic number theory
and computational complexity" by J.M. Borwein and P.B. Borwein
The Mathematical Intelligencer, Vol. 11, No. 3, 1989, pp. 73-77

Stan Wagon
Is pi normal?
The Mathematical Intelligencer, Vol. 7, No. 3, 1985, pp. 65-67

J.W. Wrench, Jr.
The evolution of extended decimal approximations to pi
The Mathematics Teacher, Vol. 53, 1960, pp. 644-650

==============================================================================
Newsgroups: sci.math