Enigma machine

Enigma machines were designed to create complex coded messages that were almost impossible to crack.

Throughout World War II Germany and its allies were using Enigma machines on the battlefield, at sea, in the sky and within its secret services, to send military messages.

The Germans considered the Enigma code to be unbreakable, but Mathematicians in Poland, France and the UK developed advanced techniques that broke the Enigma code, helping to shorten the war.

Today mathematics is at the heart of all computer security – as well as attempts to break it.

Curriculum links:




Catalytic converter

A catalytic converter is a large metal box that sits underneath your car. Its job is to convert harmful, toxic fumes from the fuel in your car’s engine into less harmful emissions.

In the 1970s, there was growing concern over the health risks that these fumes posed to us. By calculating the statistical risk to our health we were able to work out the probability of these fumes causing us harm.

Catalytic converters were the answer as they help reduce the chances of us getting ill by reducing the emission of toxic fumes.   

Curriculum links:

KS3 Maths: Probability, Statistics
KS3 Science: Gas exchange systems, The particulate nature of matter, Chemical reactions
KS4 Science: Rate and extent of chemical change, Earth and atmospheric science


Marine sextant

This sextant was used as a navigational instrument by sailors in the 18th century. At this time, navigation at sea was very important, because the seas were being used by Britain to trade with other countries.

Sailor’s use latitude and longitude to find their ship’s location whilst at sea. Latitude and Longitude are measured in degrees.

Lines of longitude run from the top of the Earth to the bottom and meet at a point at the North and South Poles. The Equator has the latitude 0˚, because it is half way between the North and South Pole.

Lines of latitude circle the Earth in an east-west direction. Greenwich, England, is commonly recognised as the longitude 0˚.

Sextants were hand-held astronomical instruments for measuring angles accurately

Sailors can calculate a ship’s latitude from the position of the Sun, but to calculate longitude is more difficult. To calculate longitude you need to know the time of day at Greenwich and in the 18th century reliable chronometers (clocks) were expensive and not readily available.

Instead sailor’s used the lunar distance technique to calculate longitude.

Sextants were hand-held astronomical instruments for measuring angles accurately

How to use it

Lunar-distance involves measuring angles between the Moon and the Sun or stars, which can be done with a sextant, a pocket watch and nautical almanac.

Today satellite navigation tools, such as GPS, are the most common form of navigation for people at sea. However, navigation techniques using time, mathematics, the Moon and stars are still useful skills to know.

Lunar-distance is all about measuring angles between the Moon and the Sun or stars.

You begin by taking three measurements:

  1. The distance between the Moon and a star – in this case the Sun.
  2. The altitude of the Moon above the horizon
  3. And the altitude of the Sun above the horizon

Below deck, you spend hours carrying out calculations. First you find local time, using observations made on board the ship

Then you adjust your measurements - this is necessary because of ‘refraction’ – the way light bends as it enters the Earth’s atmosphere And also because of ‘parallax’ – the effect of observing the sky from the Earth’s surface, not its centre.

All of these calculations and adjustments give you the lunar distance. You look up this value in a nautical almanac, which tells you the time in Greenwich, London.

You now know the time on board the ship and in Greenwich. The difference between them gives you your east-west distance or longitude. This is because it takes 24 hours for the Earth to rotate 360 degrees. So 1 hour of time difference is equal to 15 degrees of angular distance.

Curriculum links

  • Trigonometry
  • Angles
  • Shape of triangles
  • Map references, latitude and longitude (Geography Key Stage 1 and 2)
  • nPossible links to computer programming activities i.e. instructions/directions? Too tenuous?
  • nActivity link – phases of the moon/planispheres?


Ishiguro storm model

Shizuo Ishiguro, an electrical engineer and mathematician, developed this machine to simulate the North Sea and increase our ability to predict the impact of storm surges on our coastline.

It simulates a body of water using flows of electricity, which pass over an electrical grid and demonstrates how specific weather conditions affect the ocean.

There was a huge increase in funding for this mathematical research after a severe storm with winds of up to 126mph caused a surge from the North Sea on the 31st January 1953. It hit the UK and parts of northern Europe, flooding 24,000 homes and killing more than 2500 people.

Research continues today with oceanographers using a range of engineering and mathematical techniques to collect and analyse vast quantities of data about the weather and the oceans. This research is helping us to predict and detect the effects of global climate change.

Curriculum links:

KS3 & KS4: Algebra, statistics and probability
KS3: Computing
KS3: Earth and atmosphere and Waves
KS4: Earth and atmospheric science