Pi Day

Pi Day

Written by Melissa Croft
Illustrated by Julia Bains
As you may know, today is Pi Day! It is celebrated on March 14th as the date could be written as 3/14, resembling the first three digits of pi (π). We all have many plans for this special day, such as running a pi memorization contest, making pie with your grandma, wearing all your cool pi t-shirts, but you probably never thought of throwing frozen hotdogs! That’s right, pi can be calculated by throwing frozen hotdogs!

This cool experiment is based off of Buffon’s Needle Problem (he used needles instead of hotdogs, but in our opinion it’s more fun with the frozen hotdogs). The goal is to calculate the probability that a falling needle (or hot dog) will land on a line – these lines are parallel to each other with an equal distance between them. With his fancy equations, Comte de Buffon gets the probability using different distances between the lines. He concludes that when the distance between the lines is the same as the length of the needle, the probability of the needle landing on one of the lines is equal to 2/π, which is equal to about 0.637, or 63.7%; just moving that equation around and dividing 2 by 0.637 will give you the value of π, 3.14!

You can even do this experiment in your own house! All you need to do is get those frozen hotdogs—or use your grandmother’s—and tape to make the lines on the kitchen floor; all you have to do next is throw the frozen hotdogs! And if you’re not fond of eating slightly used hotdogs afterwards, you can always replace them with pencils, baguettes, or even toothpicks if you want to go for something more travel size. The equation for the probability can be rearranged to: π = (number of tosses) x (number of crosses)/2, where the number of tosses equals the total number of frozen hotdogs thrown, and the number of crosses is the number of hotdogs that land on a line.

One variation of this experiment involves throwing a polygonal (multi-sided) object instead of needles with the distance between the taped lines being longer than the length of the object’s side. The probability of one of the edges of the object crossing a line would = perimeter of the polygon/(π x distance between the lines); this equation can be rearranged to get the value of π as well!

Another variation of this experiment is known as Buffon’s Noodle Problem where the needle is curved—if you prefer throwing noodles instead of frozen hotdogs, this experiment is for you! The noodle or curve can be converted to many straight lines (or needles). The expected number of needles crossing the lines only depends on the length of the noodle and the distance between the lines. When this estimation of the noodle is used in Buffon’s equations, the result is that the probability of the noodle crossing a line = (2 x length of noodle) ÷ (π x distance between the lines), which you can once again rearrange to find π!

We hope that you enjoyed reading this article and that you just as much fun celebrating Pi Day this year and every coming year! Just in case some of you may forget (we doubt you would though), we would like to send a gentle reminder to mark your calendars for Pi Approximation Day, July 22nd!