Pi calculated to ‘record number’ of digits

By | January 11, 2010

PiA 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. … 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. “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. …

via BBC News – Pi calculated to ‘record number’ of digits.

Facts about pi:

Pi is the number of times a circle’s diameter will fit around its circumference. Most people would say that a circle has no corners, but it is more accurate to say that it has an infinite number of corners. The sequences of digits in Pi have so far passed all known tests for randomness.

Here are the first 100 decimal places of Pi

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

The fraction (22 / 7) is a well-used number for Pi. It is accurate to 0.04025%. Another fraction used as an approximation to Pi is (355 / 113) which is accurate to 0.00000849% A more accurate fraction of Pi is (104348 / 33215). This is accurate to 0.00000001056%.

Pi occurs in hundreds of equations in many sciences including those describing the DNA double helix, a rainbow, ripples spreading from where a raindrop fell into water, general relativity, geometry problems, waves, etc. There is no zero in the first 31 digits of Pi. Pi is irrational. An irrational number is a number that cannot be expressed as a ratio of integers. In 1991, the Chudnovsky brothers in New York, using their computer, m zero, calculated pi to two billion two hundred sixty million three hundred twenty one thousand three hundred sixty three digits (2, 260, 321, 363). They halted the program that summer.

The Pi memory champion is Hiroyoki Gotu, who memorized an amazing 42,000 digits. …

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