Page last updated at 08:24 GMT, Wednesday, 6 January 2010

Pi calculated to 'record number' of digits

By Jason Palmer
Science and technology reporter, BBC News

Pi
Pi appears in a wide range of formulae and natural phenomena

A computer scientist claims to have computed the mathematical constant pi to nearly 2.7 trillion digits, some 123 billion more than the previous record.

Fabrice Bellard used a desktop computer to perform the calculation, taking a total of 131 days to complete and check the result.

This version of pi takes over a terabyte of hard disk space to store.

Previous records were established using supercomputers, but Mr Bellard claims his method is 20 times more efficient.

The prior record of about 2.6 trillion digits, set in August 2009 by Daisuke Takahashi at the University of Tsukuba in Japan, took just 29 hours.

However, that work employed a supercomputer 2,000 times faster and thousands of times more expensive than the desktop, running Linux, that Mr Bellard employed.

Precision targeted

These herculean computations form part of a branch of mathematics known as arbitrary-precision arithmetic - simply put, knowing a given number to any amount of decimal places.

It is hard to overstate just how long the currently determined pi is; reciting one number a second would take more than 85,000 years.

"I got my first book about Pi when I was 14 and since then, I have followed the progress of the various computation records," Mr Bellard told BBC News.

But it is not simply the number that interests him.

"I am not especially interested in the digits of pi," he wrote on his website.

It's more than just for the fun of it - pi is a way of testing a method
Ivars Peterson
Mathematical Association of America

"Arbitrary-precision arithmetic with huge numbers has little practical use, but some of the involved algorithms are interesting to do other things."

Mr Bellard plans to release a version of the program he used to do the calculation, but says that carrying on with any further billions of digits "will depend on my motivation".

Ivars Peterson, director of publications at the Mathematical Association of America, said that the result is just the latest in a long quest for a longer pi.

"Newton himself worked on the digits of pi and spent a lot of time using one of the formulas he developed to get a few extra digits," Mr Peterson told BBC News.

In modern times, pi has served as more than just a simple but lengthy constant, however.

"People have used it as a vehicle for testing algorithms and for testing computers; pi has a precise sequence of digits, it's exactly that, and if your computer isn't operating flawlessly some of those digits will be wrong," he explained.

"It's more than just for the fun of it - pi is a way of testing a method and then the method can be used for other purposes."



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