Twisted: Sophie Duncan explains the secret of Mobius strips
The glass in the picture has been twisted into a Mobius strip. The strip was discovered, by August Mobius, in the mid 19th century.
They are fun to make and explore. Take a strip of paper with a length more than twice the width (typical dimensions used for these experiments were 15cm x 5cm). Hold the paper in a loop, as if you were making a paper chain.
Before joining the two ends, twist one by 180 LESS THAN (a half-twist). Explore your Mobius strip by making a mark on the edge. From the mark, run your finger along the edge and you find that it returns to the mark, indicating that the strip has only one edge.
Draw a line along the centre of the strip. You should find that there is only one surface, as your line finishes where it began.
Guess what will happen when you cut along the line. You should end up with a much bigger loop, which still has a twist in it.
Make a new Mobius strip and cut it along a line one third in from the edge.
Carry on cutting until you reach your starting point. You should end up with two linked loops, one of which is twice as long as the other.
Experiment using Mobius strips with two, three or four half-twists.
Joining strips together can lead to other discoveries. Take two Mobius strips, one with a clockwise half-twist, and the other with an anti-clockwise half-twist. Join them at 90 LESS THAN to each other. Now cut along the centre of each strip. You should create two linked hearts. What other shapes can you make?
Mobius strips have even been used in industry. Conveyor belts with a half-twist ensure that both sides of the belt get equal wear. This means that the conveyor belt lasts twice as long.
Sophie Duncan is project manager for science at the BBC www.bbc.co.ukscience