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Note: This activity is written for people in the southern hemisphere. Northern hemisphere mathematicians can still do this activity, but they will need to swap north and south.

Safety: Ask an adult for permission before heading outdoors. Before you go, check the weather forecast and dress for the conditions. Protect yourself from the sun by wearing a hat, shirt, sunglasses and sunscreen.

You will need

• Long, straight stick (a broom handle is perfect)
• 1 m string
• Plasticine
• Compass
• Tape measure
• Pair of compasses
• Pens
• Ruler
• A3 paper (or two A4 sheets taped together side-by-side)

This activity works best on only two days a year – the spring equinox (which falls around 23 September), and the Autumnal equinox (which falls around 20 March). However, it will work quite well for a week or two around those dates.

For this activity to work, you have to set it up before 12.00 pm (noon) and the day must be sunny.

What to do

Outside

1. Stick a heavy blob of plasticine to the end of a metre of string. This device is called a plumb bob.
2. Find a place outside in direct sunlight where the ground is soft, flat and level. Drive your stick into the ground so it stands up on its own.
3. Hold one end of the plumb bob to the top of the stick. The plumb bob will point straight down; use this to make sure the stick is pointing straight up. Adjust it until you’re happy it is straight.

   

4. Use the tape measure to measure from the top of the stick to the ground in centimetres. Write this distance down.
5. Use your compass to find south. Stretch out a metre of tape measure and place the end at the bottom of the stick so it forms a line pointing south.
6. Watch the shadow of the stick. It should get smaller and circle towards the tape measure. As soon as the tape measure and the shadow line up, measure the length of the shadow in centimetres. Write this distance down.

Inside

7. Get a sheet of A3 paper, and put it on a desk in front of you with the shorter side closest to you.
8. At the bottom of the page, draw a circle with a radius of about 10 cm. This circle will represent the Earth.
9. Take the height of the stick (Step 4) and divide by 10. For example if your stick was 150 cm high: 150 cm ÷ 10 = 15 cm.
10. Starting at the top of the circle, draw a line that’s exactly that length, extending towards the top of the page. Where the line touches the circle represents your position on the Earth. Write ‘me’ next to that point.
11. Take the length of the shadow (Step 6) and divide by 10. For example, if your shadow was 80 cm: 80 cm ÷ 10 = 8 cm.

    

12. Starting at the point where the other line is touching the circle, draw a second line so it makes a right angle (it doesn’t matter whether it goes left or right). Make this new line the length you just calculated in Step 11.
13. Join the ends of these two lines to make a right-angled triangle.
14. Draw a line that cuts the circle in half. This line must run parallel to the long side of the triangle. This line represents the Earth’s equator.
15. Draw another line that cuts the circle into quarters. This line must be at right angles to the equator. This represents the line connecting the Earth’s poles.
16. Find where you wrote ‘me’. How close is your position to the equator? How close is your position to the South Pole?

What’s happening?

This activity measures the angle between the ground and the Sun. This angle changes throughout the day, with the Sun at the horizon at dawn and dusk, and high in the sky at noon. The measurement also changes throughout the year – in summer, the southern half of the world is tilted towards the Sun. In winter, the south pole is tilted away from the Sun. There are only two days a year where the Earth is not tilted with one end closer to the Sun. These two days are called the equinoxes, and they occur in September and March, when the seasons are changing.

On the equinox, the Sun is sitting directly above the equator, which makes calculating latitudes a lot easier. After the equinox, the Earth tilts, and the Sun no longer sits directly above the equator – in Summer, the Sun is directly above a point somewhere in the southern tropics. You can still calculate your latitude when it is not the equinox, but the calculation is more complicated.

Real-life maths

People have known that the Earth was round for thousands of years, and they have used this fact to calculate latitude. Using the Sun to calculate latitude is quite difficult, because the Sun moves around throughout the day and the year. However, the stars are a lot more predictable, and one star in particular is very useful. Polaris, the North Star, sits directly above the North Pole. If you can measure the angle to Polaris, you can work out your latitude. Unfortunately, you can only see Polaris if you are in the northern hemisphere.

Latitude only tells you how far north or south you are. In order to know exactly where you are on the Earth, you also need to know how far east or west you are. This measurement, called longitude, is just as important for navigating as latitude, but is much more difficult to measure. Captain Cook had an experimental clock on his second and third journeys that he used to calculate longitude.

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