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How long is a piece of paper?

Posted: Friday, 10th May 2013

How long is a piece of paper?

JUST how many times can you fold a piece of paper in half?

The BBC’s The One Show set out this week to find out with the help of Manchester Metropolitan mathematician Nicolette Rattenbury.

For a standard piece of A4, it is mathematically impossible to fold it more than seven times, explained Dr Rattenbury, because “every time you make a fold, the paper shrinks in length and doubles in height at an exponential rate”.

If The One Show wanted to set a new world record for 13 folds of a single piece of paper, she said, they needed to refer to a mathematical formula conceived by Californian Brittany Gallivan in 2002.

T is the thickness of paper and n is the number of folds you wish to achieve - in this case, 13,” Nicolette told the programme.

Calculating that they would need at least 2,000m of paper, the Nicolette, a specialist in numerical methods and computation, set off with the BBC team to the 34km tunnel under the Kielder Reservoir in Northumbria.

Despite being pregnant, Dr Rattenbury spent the afternoon underground helping fold a 3km length of paper 58millionths of a metre thick an amazing 12 times and very nearly made a 13th fold.

Dr Keith Miller, Head of Computing Mathematics and Digital Technology at MMU said: “Well done to Nicolette for bringing mathematics to the fore in this record attempt. It’s encouraging to see a mathematical formula on a mainstream TV programme.”

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