Pi Toss Probability

Time: 20 minutes

What you need:

• Toothpicks

• Paper

• Ruler

• Pencil

• Calculator

What you do:

1. Lay your piece of paper down, horizontally in front of you.

2. Take your ruler and draw two straight parallel lines on your paper—make sure the lines are two toothpicks away from each other.

3. Start randomly tossing the rest of the toothpicks onto the paper one at a time.

4. Once you toss all of the toothpicks, count the total number that you tossed. Then count the number of toothpicks that touch or cross one of the lines your drew.

5. Divide the total number of toothpicks you threw by the number that touched a line.

6. Your answer or quotient is your approximation of pi.

Questions to ask:

1. How close did you get to the true approximation of pi—3.14?

2. Does tossing more toothpicks get you closer to the approximation?

3. Try tossing just 10 toothpicks, then 50, then 100. How do you results change each time?

What's the science:

Pi has been approximated for over 4,000 years. Over time, we have gotten closer to its value, but Pi's value will never be known fully because it's an irrational number that continues forever and never repeats. The ancient Greeks estimated pi by dividing a circle's circumference by it's diameter, but there are many fun ways to approximate the number.

The method we used to calculate pi in this activity is called Buffon's Needle. It was discovered by George Lois Leclerc, the Count Buffon, around 300 years ago. He was inspired by a simple game of probability where a player tossed a coin onto a tile floor and bet whether it would land entirely inside the tile or touch the edge. From this, he developed a formula for approximating pi using a repeated random sampling that gets closer to pi the more repetitions occur.