The Big Question: How Close Have We Come to Knowing the Precise Value of pi?

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Why are
we asking this now?

A French computer
programmer has calculated pi to a world record of almost 2,700 billion
decimal places. Fabrice Bellard said he did it for the programming
challenge rather than any particular interest in this infinitely
long number. All the more remarkable is that he did it on a desktop
computer costing less than £2,000. It took 131 days to complete
the calculation and the resulting number took up more than 1,000
gigabytes of memory on his hard drive. Downloading it would take
10 days and reciting it aloud would take about 49,000 years.

What was
the old record?

It was achieved
using a multi-million pound supercomputer at the University of Tsukuba
in Japan last August. Mathematician Daisuke Takahashi calculated
pi to 2,577 billion decimal places. But his computer was roughly
2,000 times faster at processing data than Bellard’s machine. The
Japanese supercomputer calculated pi at a speed of 94.2 teraflops,
which is 94.2 trillion floating point operations or calculations
per second. It took 29 days.

What exactly
is pi?

As every schoolchild
should be able to describe, pi is the ratio of the circumference
of a circle to its diameter. In other words, divide the distance
around the edge of a circle by its diameter – a straight line
through its centre connecting one edge to another – and you
always get the same constant, denoted by pi. The problem is that
this number is infinitely long. For most purposes the value of pi
can be estimated to two decimal places, i.e. 3.14. But keep dividing
the circumference by the diameter and you soon get to 3.14159265358979323846.
Keep on dividing and you will eventually get to the number achieved
by Bellard.

Is there
another way of describing this number?

Sometimes it’s
denoted as 22/7 [i.e. 22 over 7] which is an approximation. In Europe
this is celebrated by assigning 22 July as pi Approximation Day.
In the US, however, they celebrate pi on 14 March – World pi
Day – which of course in American date notation is written
as 3/14. Either way, you have two opportunities in the year to celebrate
the cerebral pleasures of pi.

Why does
pi fascinate people so much?

It fascinates
experts because it is a number that is considered both irrational
and transcendental. It is irrational because it cannot be written
as a simple ratio of whole numbers and transcendental because pi
is living proof that you cannot square a circle. "The mathematics
of pi is often rather pretty," explained Ian Stewart, professor
of mathematics at Warwick University. "All numbers are interesting
but some are more interesting than others and pi is the most interesting
of the lot."

When did
we first learn of pi?

It seems to
go back to the ancient Babylonians. When the town planners of Babylon
began to build the city they took a keen interest in geometry and
it became evident to them as early as the 20th century BC that when
any circle’s circumference was divided by its diameter the resulting
number was always about three. In fact they calculated the value
of this ratio as equal to 25/8 [25 over 8] which is 3.125 –
within 0.5 per cent of the true value of pi.

Interestingly,
a less exact value of pi is given in the Bible (Kings 7:23) which
described a round basin with the dimensions: 10 cubits in diameter
and 30 cubits in circumference. This conveniently results in pi
being a nice round number – three – but it is quite inaccurate.
Mathematicians would reel back in horror at such a tidy calculation,
which is why Professor Fink in an episode of The Simpsons managed
to gain the full attention of hall full of babbling scientists when
he shouted "pi is exactly three!"

Read
the rest of the article

January
9, 2010

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