a071  0809  08 Jun 89
PM-Big Pi Slice,0146
Mathematicians Calculte Pi to 480 Million Decimal Places, University
Says
    NEW YORK (AP) - Two mathematicians have calculated pi to 480 million
decimal places, more than doubling the mark set last year, according
to Columbia University.
    Pi is an infinite string of numbers that is the ratio of the
circumference of a circle to its diameter. It is roughly equal to 22
divided by seven.
    Gregory and David Chudnovsky, brothers who are associate research
scientists at Columbia, made their calculation using supercomputers,
the university said in a statement.
    Their approach will allow mathematicians to grow the number from its
middle or end without having to start at the beginning, the
university said.
    The number they produced, if printed out, would be 600 miles long,
the university said.
    It surpasses a calculation of about 201 million decimal places made
last year by a Japanese researcher, Columbia said.
    
 
AP-NY-06-08-89 1104EDT
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a219  1222  08 Jun 89
AM-Big Pi Slice,0371
Pi Reportedly Calculated to Record 480 Million Decimal Places
By MALCOLM RITTER
AP Science Writer
    NEW YORK (AP) - Two researchers say they have cut themselves a
record slice of pi: 480 million decimal places of one of the most
famous numbers in mathematics.
    That exceeds the mark of about 201 million decimal places produced
last year in Japan, David Chudnovsky of Columbia University said
Thursday.
    Pi is the ratio of the circumference of a circle to its diameter.
The infinite string of digits begins with 3.14159, and contains no
obvious pattern.
    The newly calculated number would stretch for 600 miles if printed,
Columbia University said.
    Chudnovsky and his brother Gregory, associate research scientists at
Columbia, came up with the number after devising a new algorithm,
which is a series of mathematical steps.
    The algorithm lets researchers calculate more and more decimal
places for pi by simply adding to an existing string, rather than
having to start from scratch, Chudnovsky said.
    It also has a self-correcting feature that can check whether the pi
calculation is on the right track while the calculation is in
progress, he said.
    The researchers checked their calculation by running the algorithm
through two supercomputers with different hardware and software,
Chudnovsky said. When the results were compared, ''everything
perfectly fitted together.''
    So what good is knowing this number?
    ''We can use it as a very stringent test for testing the performance
of hardware and software,'' said Chudnovsky, who called pi
calculations ''the ultimate stress test.''
    And by calculating pi out to great lengths, researchers can
investigate whether the string of digits is random or contains some
hidden pattern, he said.
    ''We sort of see more of the tail of the dragon,'' he said.
    The new work is to be presented next week at a conference on
computers and mathematics at the Massachusetts Institute of
Technology.
    Peter Borwein, associate professor of mathematics at Dalhousie
University in Halifax, Nova Scotia, Canada, said the new work appears
to be a record.
    Tackling the digits of pi ''has become something of a benchmark in
computational sophistication,'' he said in a telephone interview.
    ''It seems like since there have been computers, people have been
using them to compute the digits of pi.''
    
 
AP-NY-06-08-89 1513EDT
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