A MATHEMATICAL puzzle that has taxed human minds since the time of the Bablyonians has been solved as never before: a Japanese team has smashed a world record by calculating the value of pi to more than a trillion decimal places.

The number, which runs to 1.2411 trillion places, is so huge that it would fill a book 135 times the height of the Eiffel Tower and take almost 40,000 years to recite.

Pi is the ratio between a circle’s circumference and its diameter, and is critical to mathematical calculations in fields as diverse as chaos theory, astronomy and economics.

This mind-boggling achievement, however, is no practical use whatsoever.

A value accurate to just 37 decimal places is sufficient for mathematicians to calculate the radius of the entire universe, with a margin of error the size of a hydrogen atom.

The sum was worked out by a team from Tokyo University led by Professor Yasumasa Kanada, using a Hitachi supercomputer that ran for more than 400 hours.

It improves six-fold on the previous mark recognised by the Guinness Book of Records — which Professor Kanada calculated to 206.158 billion places in 1999. The value is generally known to schoolchildren as 3.1416 but it can in theory be calculated to an unlimited number of places, given a powerful enough computer and sufficient time.

The computer that Professor Kanada used for the sum was capable of performing two trillion calculations per second.

Roger Webster, a mathematician at Sheffield University, said that while the experiment offered proof of the power of Professor Kanada’s computer, it would be of little practical use to scientists or mathematicians.

“There is no value at all in having such a precise answer,” he said.

“It is a great achievement as an intellectual exercise, and it shows how good the computer is, but that really is all.”

The first attempts at calculating pi were made by the Babylonians in 2200 BC, who came up with a value of 3.125.

In 250 BC, Greek mathematicians produced a much closer estimate of 22/7 (3.14285), which was commonly used in schools as a convenient shorthand before the widespread advent of pocket calculators.

A Dutch mathematician, Ludolph van Ceulen, worked the ratio out to 35 places in the 16th century, and had the figures inscribed on his tombstone when he died in 1610.

Computers extended the sum still further, with the millionth place being cracked in 1973 and the two millionth in 1981.

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