## Introduction: Calculate Pi by Throwing Sausages

This method of calculating pi is the wurst...

...but it is surprisingly accurate considering it only requires pen, paper and sausages!

Technically you can use anything straight and long, but pencils don't taste as good.

## Step 1: Set Up Your Sausage Throwing Arena

Measure your sausages and draw straight lines on your paper a sausage length apart.

You might want to use several sheets to create a bigger area for throwing your sausages onto depending on their size.

## Step 2: Throw Your Sausages!

Throw your sausages on to the paper!

Keep track of how many are crossing a line and how many are not. In the picture above, there are 7 sausages crossing a line and 3 sausages (circled in red) which are not.

Write down how many of your sausages are crossing lines. Throwing 10 sausages at a time makes it easier to keep track.

## Step 3: Throw Lots of Sausages!

The more sausages you throw, the closer your final answer will be to pi! I threw a total of 400 sausages to get my answer.

Add up how many sausages you threw compared with how many crossed a line. In the next step, we'll put these numbers into an equation to find pi!

Top tip: Gather up and reuse the same 10 sausages ;)

## Step 4: Calculate Pi

To calculate pi, we will use this approximation:

Probability ≈ 2 / π

Where the probability is the likelihood of a sausage landing on a line, worked out like this:

Probability = (Number of sausages crossing lines) / (Total number of sausages thrown)

Rearranging this to find pi, we get

π ≈ (2 x Total number of sausages thrown) / (Number of sausages crossing lines)

By putting in our numbers, we get

π ≈ (2 x 400) / 254 π ≈ 3.14960

Which is pretty close 3.14159... the actual value of pi!

## Step 5: Why This Works

The maths behind this is based on Buffon's Needle Problem, an 18th century mathematical problem about geometric probability. You can read more about it here.

What we're doing is a Monte Carlo method for approximating π, which involves a lot of integrals and statistics unless you set up the experiment the way we did here, with our lines being equal in length to our sausages.

Pi comes into it because there are 2π radians in a circle and our sausage is essentially the diameter of an imaginary circle which is intersecting with the lines.

If you want to learn more, there are some great videos out there which try to explain the maths in more detail like this great one from Numberphile.

I hope you enjoy your sausage pi!