Science, Maths & Technology
  • Video
  • 5 mins
  • Level 1: Introductory

Mathematical striptease

Updated Thursday 5th February 2009

Does maths get your knickers in a twist? Watch this video to see how maths can hold the solution to some everyday problems

Here's a challenge: can you turn your shirt inside out if your hands are tied together?

Discuss this video, and watch other thought-provoking films on the OU YouTube channel.

The explanation

Well it's obvious how George the first turned his shirt inside out, but you might be wondering why it worked when George the second did it with his hands tied together. And should the pole really have caused George the third so much trouble? Like so many things, it can all be explained by good old mathematics.

 

George the second removes shirt Copyrighted image Icon Copyright: Production team George’s task of turning the shirt inside out with his hands tied together may be simpler than it seems. His shirt comes off his head onto his arms and down the rope.

While it is on the rope, it’s now the right way around…but it’s not yet on George.

However, while it is on the rope it can fairly easily be turned outside in again, by pushing the shirt down one of its own sleeves.

Once back on the rope, it is now inside out – but not yet on George.

He can then reverse his first move and put it back on again, which in the process turns it right way out.

Maths isn’t just about numbers. There’s a major area of maths called topology. This is the study of the properties of space.

It seems that topologists don’t care much about size, texture, shape, distance – they’re interested in very abstract notions of space.

It’s perhaps easier to imagine a topologist's view of the world as made of infinitely stretchable clay. So a cube can be made into a sphere, or a pyramid – so they are the same. A ring can be made into a loop, a doughnut shape, even a doorway – so they are all the same. However, a cube CAN’T be made into a ring without tearing a hole in the middle – so they are not the same.

Basically, it seems that in topology any object is equivalent to any other object if, when it is stretched/deformed, it can take the same shape without tearing apart or having distinct parts stuck together.

Okay – now we think that a topologist might be able to solve George the third’s problem. Like George the second, he’s got his shirt on inside out, and his hands are tied together. However, he’s also got his hands around a pole.

Let’s start with how a topologist might describe George the second. To a topologist:

  • George the second (with his rope) is just part of a ring – formed by his arms and the rope.
  • His head and lower torso are just odd, unfortunate lumps on the ring.
  • Around this ring is another ring – his shirt – which could be stretched and rolled.
  • His ‘shirt’ ring could easily twist around – turning outside in and inside out.

So if his head and body are shrunk down then his shirt can slide all along the ring, made of rope and arms (with a tiny head and tiny body), without any fuss, like his head or body getting in the way.

The closest George the second gets to this in the real world is when he’s removed the shirt over his head and the shirt is sitting on the rope in front of him – where is can easily twist around and be turned outside in – and then place back on again.

Topology of George the third Copyrighted image Icon Copyright: Production team To a topologist, George the third is just the same as George the second – except the ring his arms and rope make now also circles around a pole (think of it as another infinite ring).

Now, a topologists could repeat what happened with George the second. He shrinks his head and torso – allows the shirt to sit on the ring and twist outside in again. The pole seems irrelevant to completing the task in the world of topology.

Of course, George is not an ideal topological object – but subject to the constraints of the real world (he can’t be stretched and shrunk).

The fact that George the third can’t morph the shape of his body into a ring may mean he'll be stuck around the pole for some time…

Though you might want to think about this: if the shirt had been very stretchy would a real world George have managed to turn it outside in and put it back on again (if for example, he could pass his body down the sleeve?)

 

What could you do next?

  • Can you get out of the George the third challenge – post your clips on the 'Mathematical Striptease' You Tube page
  • Post clips of other topological challenges
  • Check out the mathematics courses at the Open University
 

For further information, take a look at our frequently asked questions which may give you the support you need.

Have a question?

Other content you may like

Diary of a data sleuth: Getting to grips with the census data article icon

Science, Maths & Technology 

Diary of a data sleuth: Getting to grips with the census data

With the recent release of key statistics around the UK's 2011 census by the Office for National Statistics, our resident data sleuth set out to see what he could find.

Article

Science, Maths & Technology 

Working mathematically

This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process.

Free course
10 hrs
Differential equations Copyrighted image Icon Copyright: Used with permission free course icon Level 2 icon

Science, Maths & Technology 

Differential equations

This free course, Differential equations, extends the ideas introduced in the course on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The course assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

Free course
16 hrs
When should you use a stacked area chart? Copyright free image Icon Copyright free: wokandapix article icon

Science, Maths & Technology 

When should you use a stacked area chart?

... or why you should never use stacked area charts, according to Dr Drang.

Article
Symmetry Copyrighted image Icon Copyright: Used with permission free course icon Level 2 icon

Science, Maths & Technology 

Symmetry

We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This free course, Symmetry, explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.

Free course
20 hrs
Starting with maths: Patterns and formulas Copyrighted image Icon Copyright: Used with permission free course icon Level 1 icon

Science, Maths & Technology 

Starting with maths: Patterns and formulas

Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This free course, Starting with maths: Patterns and formulas, explores some of these patterns, from ancient number patterns to the latest mathematical research.

Free course
5 hrs
Using vectors to model Copyrighted image Icon Copyright: Used with permission free course icon Level 2 icon

Science, Maths & Technology 

Using vectors to model

This free course, Using vectors to model, introduces the topic of vectors. The subject is developed without assuming you have come across it before, but the course assumes that you have previously had a basic grounding in algebra and trigonometry, and how to use Cartesian coordinates for specifying a point in a plane.

Free course
16 hrs
Prices Copyrighted image Icon Copyright: Used with permission free course icon Level 1 icon

Science, Maths & Technology 

Prices

This free course, Prices, looks at a wide variety of ways of comparing prices and the construction of a price index. You will also look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You will also look at the important statistical and mathematical ideas that contribute to the construction of a price index.

Free course
20 hrs
Real functions and graphs Copyrighted image Icon Copyright: Used with permission free course icon Level 2 icon

Science, Maths & Technology 

Real functions and graphs

Sometimes the best way to understand a set of data is to sketch a simple graph. This exercise can reveal hidden trends and meanings not clear from just looking at the numbers. In this free course, real functions and graphs, you will review the various approaches to sketching graphs and learn some more advanced techniques.

Free course
20 hrs