## Coins around the equator

By David Shaw, 11 April 2016

Label your jar clearly and start collecting coins!

How much money would it take to put a line of coins around the equator? With a bit of research and a bit of maths, you’ll soon know the answer!

### You will need

- Silver coins
- Jar
- Cardboard
- Fine marker
- Paper
Make a one-metre line of coins.

- Masking tape
- Scissors
- Tape measure

### Collecting coins

First, collect some silver coins to measure. If you don’t have enough, here’s a handy technique to try.

- Take the lid off a jar.
Tally up the value of one metre of coins.

- Use a fine marker to trace around the lid onto cardboard.
- Cut out the lid shape and cut a slot in it for coins to fit through. Use a 50 cent coin to check if the slot is big enough.
- Tape the cardboard lid to the top of the jar.
- Place a sign near the jar saying ‘silver coins for maths!’
- Ask people to donate their silver coins to help you with your investigation. Make sure you don’t leave the jar somewhere it could get stolen!
- Hopefully after a few weeks you’ll have lots of coins to work with.

### Gathering data

- Stick a short piece of masking tape to the ground.
- Measure one metre from your tape line and tape a second line.
- Lay a line of silver coins between the two tape marks.
- Count up the value of the coins in your line and write it down.
- Lay down two more lines of silver coins between the two marks, recording their values too.
- Calculate the average value of a one-metre line of silver coins:

Average money per metre = (value of line 1 + value of line 2 + value of line 3) / 3

### Putting it together

- Search the internet or research at your library to find out how far it is around the equator. Convert the distance into metres. (For example, if you find the answer in kilometres, you will need to multiply the distance by 1000 to convert to metres.)
- Calculate the value of coins needed to go all around the world:

Money around the world = number of metres x money per metre.

- After you’ve finished, work out what you’re going to do with your coins. Maybe you should do something nice for everyone who gave you money!

### What’s happening?

This question is a bit silly – no one is ever going to put a line of coins around the equator. But the techniques you used to answer it are very useful in real life.

This sort of question is known as a Fermi problem. It is named after Enrico Fermi, a famous nuclear physicist. Enrico was very good at breaking down a question into smaller questions and then combining those answers to answer the big question. During the Manhattan project, Enrico estimated the size of a nuclear explosion by dropping little pieces of paper on the ground!

**Extension:** A line of fifty-cent coins around the equator is worth more than the same distance in five-cent coins. What’s the difference in value?

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