Mathematicians bake pies for their favourite number – Pi! Credit: ©iStock.com/Mizina
Do you have a mathematician in your life? Chances are, they’re a big fan of the number Pi. Celebrate Pi Day with them on 14 March!
Pi is a number that helps us work with circles. You might have seen it written as ‘π’ or given the value 3.14 or 3.14159…on and on it goes. To understand where Pi comes from, first imagine a pie: the circular distance around the crust is called the circumference. Now imagine slicing the pie in half: this straight distance across is called the diameter.
Early on, mathematicians from around the world discovered that a circle’s circumference is always exactly Pi multiplied by its diameter. This works for circles of any size, from single atoms all the way up to the entire universe!
Pi is also famous because it’s an irrational number. If you try to write it out, the digits keep going forever, and they never get stuck in a repeating pattern. Many more secrets hide in its digits, and mathematicians are still trying to answer questions about it.
Now you know a bit more about Pi, you can plan your own Pi Day celebration. And what better way to celebrate than by calculating that famous, circular number, Pi!
You will need
- 2 sheets of paper
- About 15 toothpicks
- Pen or pencil
- Ruler
- Calculator (optional)
What to do
Place one sheet of paper on a table and measure a ‘toothpick-length’ distance away from the top. You can do this by putting 2 toothpicks near each other, each pointing straight down the page.
Mark the endpoints of the 2 toothpicks with a pen or pencil.
Rule a line through the two marks – it should be parallel with the top of the page.
Use the two toothpicks to measure one toothpick length below the line you just drew. Rule through the dots like you did last time to make another parallel line.
Repeat step 4 until the sheet of paper is filled with parallel lines, each a toothpick length apart.
Place the lined paper on the floor and gather 15 toothpicks.
Stand over the paper and randomly drop the toothpicks – one by one or all at once – onto the paper.
Count how many toothpicks fell completely onto the lined sheet of paper (you can re-drop the toothpicks that hit the paper and then fell off). Write this number down on the other sheet of paper and label it ‘total toothpicks’.
Count how many toothpicks touched or crossed a line. Write this number down and label it ‘crossed toothpicks’.
It’s time to estimate Pi! First, multiply the number of total toothpicks by 2. Next, divide the answer by the number of crossed toothpicks. This formula looks like:
Pi ≈ 2 x total toothpicks ÷ crossed toothpicks
Getting a better answer
Were you close to 3.14? Since this experiment involves random chance, you’re unlikely to get a perfect estimate of Pi on the first try. But you can improve your estimate! Try another round of dropping, and add up the total toothpicks and crossed toothpicks for both rounds before you use the formula.
What’s happening?
Many toothpicks make a circle
This experiment has a name: Buffon’s Needle. Count Buffon wondered what the probability was of dropping a needle into cracks in the floor. This may seem like a strange question, but it was inspired by a game he was playing with his friends.
While conducting his experiments, Buffon noticed an important thing: a toothpick can land at any angle from 0 to 360 degrees – in other words, a full circle. So, when enough toothpicks are dropped, it’s a bit like dropping a full circle that has a toothpick length’s diameter. And we know that when circles and diameters are involved, Pi will pop up!
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