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Marcus du Sautoy's
Sexy maths JOE MdAREN
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Twists and turns that make a rollercoaster ride
Twists and turns that make a rollercoaster ride
love rollercoasters. It's not just the Grand National ride then at Becher's of making this twist appears when you
thrill ofthe ride. If you're a nerdy Brook the paper is twisted 180 degrees as take a pair of scissors and cut the shape
mathematician like me, it's the the tracks run under and over each other down the line that you've just drawn.
buzz of all the geometry and before they arejoined to the track at the Instead of the two loops of paper that
calculus that has gone into beginning ofthe ride. you'd expect by cutting something in half,
constructing a ride that pushes The Mobius strip has some very the result is a single piece oflooped paper
things to the limit. But there is one curious properties. The shape has only with two twists in it.
rollercoaster in Europe that gets one edge. Put your finger on the edge of The properties of this shape have not
my blood racing more than any the strip and follow it round. You will be been exploited only by the rollercoaster
other: the Grand National in able to reach any other point on the edge. industry. Conveyor belts are often built in
Blackpool. When you race round this This means that the rollercoaster at the shape of the Mobius strip because
track you are experiencing one of the Blackpool isjust one continuous track havingjust one side means that the entire Conundrum
most exciting shapes for mathematicians: rather than two parallel tracks. surface of the belt gets the same amount IfI take a Mobius strip
the Mobius strip. Extraordinarily, the shape also has only of wear and so the belt lasts longer. The and cut it lengthways
The Grand National is a race between one side. Take a pen and start tracing a recycling symbol is based on a Mobius down the middle I get just
two trains. When you get in your carriage line along the length of the shape without strip. And the least you'd expect of the one looped piece of paper.
at the top of the ride there seems to be taking the pen off the paper. Eventually Oxford University Mathematical Society But what happens if I cut
two parallel tracks. Riders in one train can you come back to the place where you is that its scarf be knitted into the shape. this new loop lengthways
touch those in the other as they pass started. Not so surprising given that the It even has its own movie. The down the middle?
through features named after some of the paper is a loop. But the unexpected Argentine film Mabius concerns the
jumps of the famous horse race. But as the discovery is that when you look you find disappearance of a train in the
trains make the dash for the winning post that there is no side of the paper that labyrinthine Buenos Aires subway
something strange happens. The trains hasn't been drawn on. That's because the system. The mathematically minded
arrive at the stations opposite to the ones twist has ensured that this shape has only young detective assigned to the case
from which they embarked. Very curious. one side. The truly bizarre consequence concludes that the countless additions
The tracks never meet or seem to cross made to the network over the years have
"
each other. How on earth did the unwittingly created a Mobius strip on
designers create this feat? which the train is now trapped.
The effect is achieved at the infamous
Becber's Brookjump, where one track The Mbbius The disappearance of the train is a
metaphor for the political activists who
races over the top ofthe other and from
that point the tracks have swapped sides,
strip has some went missing in Argentina during the
1970s, but the maths of why a Mobius strip
. so that by the end of the ride the trains
arrive at the opposite station.
very cunous should make trains disappear is never
fully explained. Next time you are in
And it is this simple twist at Bechers properties. The Blackpool, however, remember to count
Brook that.is the key to the Mobius strip, your friends on and off the Grand
the beautiful mathematical shape that shape has only National rollercoaster. Maybe the
underpins the design ofthis track. To
construct your own Mobius strip, tear off
one edge and, Argentinians have discovered something
that we mathematicians don't know about
a long strip of paper from the bottom of
the newspaper - about 2cm in width.
extraordinarily, the shape.
'l! u!
Now join the ends up in a loop, but before only one side Marcus du Sautoy will give the Geary SlSlMl mOJ seq dooj q:mg
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you do so make a twist ofl80 degrees in Lecture tomorrow at 7pm at City
one end. If you imagine a piece of paper University, London, on his book Finding Jaded JO sdoo] OMlla8 no.x
running between the two tracks of the Moonshine JaM.SUV
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