Science -- Your Future, Scotland's Future
SCI-FUN Roadshow Exhibits -- Reuleaux Curves
SCI-FUN Roadshow Exhibits -- Reuleaux Curves
In this exhibit you learn about why some coins are different shapes to others.

Most coins are circular, but 20p and 50p coins are different. Instead of being circular, they are curved heptagons (seven-sided shapes).

All coins need to be able to roll, so that they can be used in vending machines. 20p and 50p coins can roll just as well as circular coins, even though they are not circular.

This is because they are Reuleaux curves. Reuleaux curves have curved corners and slightly curved edges, and always have an odd number of sides. This means that they are always the same width all of the way around. Circles are also the same width all the way round. This is why circles and Reuleaux curves roll.

The constant width of these coins also means that they can be identified using coin detectors in vending machines. These detectors identify coins and check they are genuine by measuring their weight, width and/or magnetism. It is, therefore, important that a measurement of width from any angle will give the same width.

Coins are made as Reuleaux curves as this makes it easier to identify them by touch only. This means it is easier to find the right coins when rummaging in our pockets or in the dark, and easier for blind people to find the right coins. UK and Euro banknotes are all different sizes too, so that blind people can recognise them, but US banknotes are all the same size, so blind people often struggle.

Another benefit of Reuleaux curved coins is that they use slightly less metal than circular coins of the same width. This means they are cheaper to produce.

Manhole covers can also be made as Reuleaux curves. A manhole cover with a non-constant width, such as a square shape, is dangerous because it can be rotated and dropped down the hole. Therefore, it is best to make manhole covers circular or Reuleaux curves, as these cannot be dropped down the hole.

Reuleaux curves were invented by Franz Reuleaux, a German engineer. He designed machines which used a series of simple mechanical motions to create a more complex motion. He invented the Reuleaux triangle to use in such machines.

1 20p and ________ coins are curved ________.
2 Why do coins need to be able to roll?
3 What property of circles and Reuleaux curves means that they can roll?
4 What group of people particularly benefit from having coins shaped as Reuleaux curves?
5 Why is a square manhole cover dangerous?
6 Why do you think a Reuleaux curve has to have an odd number of sides?

1 Get a collection of coins and spread them out on a table in front of you. Wearing a blindfold, and using only touch, see if you identify the coins. Is it easy to do? What features of each coin help you to work out what they are?
2 Make a Reuleaux Triangle. Using a pair of compasses, draw a circle. Keeping the radius the same, place the point of the compasses on the line of the last circle and draw another circle. Now place the point on the place where the two lines cross and draw a third circle. This should give you three intersecting circles. In the middle of the three circles, there will be a Reuleaux Triangle.