Before we can learn more about pi, it will help if we review a bit of geometry. In particular, we need to brush up on circles. Why? Well, we’ll get around (pun intended!) to that in a second…

The circumference of a circle is its perimeter or the length around it. The distance from the center of a circle to its edge is the radius. The distance from one side of a circle to the opposite side (twice the radius) is the diameter. The area of a circle is the number of square units inside the circle.

Since circles can vary in size, yet they all retain the same shape, ancient mathematicians knew there had to be a special relationship amongst the elements of a circle. That special relationship turns out to be the mathematical constant known as pi.

Pi is the ratio of a circle’s circumference to its diameter. Regardless of the size of the circle, pi is always the same number. So, for any circle, dividing its circumference by its diameter will give you the exact same number: 3.14159…or pi.

Pi is also an irrational number, which means that its value cannot be expressed exactly as a simple fraction. As a result, pi is an infinite decimal. Although 22/7 gives a result that is close to pi, it is not the same number.

Since mathematicians can’t work with infinite decimals easily, they often need to approximate pi. For most purposes, pi can be approximated as 3.14159. Some people even shorten it to 3.14, which is why Pi Day is celebrated on March 14 (3/14).

Interestingly, there can be no “final” digit of pi, because it’s an irrational number that never ends. Mathematicians have also proved that there are no repeating patterns in the digits of pi.

Computers have calculated pi to over three trillion digits. Here are a few representations of pi to different numbers of digits (past the decimal):

- Pi to 10 digits: 3.1415926535
- Pi to 100 digits: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
- Pi to 1000 digits: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989

Pi is an important part of many mathematical formulas. Most geometry students first encounter pi when they study circles and learn that the area of a circle is equal to pi times the square of the length of the radius. This formula — A=πr^{2 }— is sometimes described as “area equals pi r squared,” which is the basis of the old joke about pies being round, not square.

You may have noticed in the equation above and in many other places, pi is represented by (and takes its name from) the Greek letter pi (π). The Greek letter π was first used to represent pi by William Jones in 1706, because π was an abbreviation of the Greek word for perimeter: “περίμετρος.”

In school, we have Pi Day on 3.14 (March 14th). All day in math, we eat pie!!!

That sounds like OUR kind of math class, Autumn! Very sweet! Thank you for sharing about your school’s Pi Day!

for real tho

Welcome, jaeden! You’re right – that sure is a lot of pie to eat! Thanks for visiting WONDERopolis!

WOW!! Pi is pretty cool! I’m kind of hungry…

Math makes us hungry, too, Johah! We think we could eat slice of “Pi” right now! Thanks for letting us know you liked this Wonder of the Day®!

In our school, on March 14 (in other words Pi Day), we have, get ready…A PIE EATING CONTEST!

That is so cool, E.N! Have you ever been a competitor in the pie eating contest at your school? How many pies do you have to eat? What is the time limit for eating them?

WOW !!!!!!! I Didn’t know that pi was a big thing and that it has it’s own day.

We’re glad you learned some new things about pi today, John! Thanks so much for visiting this Wonder!

Wonderoplis, the story you did about pi was wonderful! I learned two new vocabulary words which were irrational, and infinite. Two new things I learned today was Pi has lasted to 3 trillion digits and there is no final digit of pi. I wonder why there is no final digit of pi. I look forward to more stories like this one!

Hello, Team McNeil 13! We like how you and so many of your classmates let us know the new vocabulary words you learn with each Wonder. We think that ROCKS!

Pi Rocks! Go Pi!

So awesome! GO PI.

We love your enthusiasm, Makayla!

I want some pi.. I mean, pie! Haahaha Cool wonder today, Wonderoplis!

Thanks so much, Wonder Friend Salma! We’re so excited that you liked our pi Wonder… and we hope you had some pie, too! YUM!

That sounds WONDERful!!! Just thinking about it I WANT PIE. Also, you did it again WONDEROPOLIS!!!!!!!! I will wonder a lot sometimes…

WONDERful, Ingrid! We are so glad to have you WONDERing with us today! Don’t forget 3/14 is Pi Day! Keep WONDERing!

I don’t know even the first 888 digets and it’s ones place is 9

Pi is a very long number, Ethan! How many digits can you remember? Thanks for WONDERing with us today!

We had pizza and pie, because pizza can also be called a pie.

Happy Pi Day, Grag! You are absolutely right! A pizza is also called a pie. Have a slice of pie for us today, Wonder Friend!

I like pizza. Its too bad I didn’t get any.

There’s always next year, Samconry!

The video was funny because the lady woke up and she started acting funny/crazy.

Terrific, Jada! We are so glad that you enjoyed this Wonder Video! We hope you had an awesome Pi Day… on Friday!

I don’t like pie, but pi is interesting! Shouldn’t computers be able to get more than a trillion, though?

Great question, Elizabeth! We agree, there has to be a super computer somewhere that can get more numbers. But, that’s a whole lot of numbers! Keep WONDERing Wonder Friend!

Next year is going to be 3/14/15 as in 3.1415. Did you know that? NO!

Pi is fun. I ate blueberry pie that day. It was yummy.

That’s awesome, Samconry! No, we did not know that. Next year is going to be a very special Pi Day! Yum! Blueberry pie sounds awesome! Thanks for WONDERing with us today!

Wow! Pi is cool. We celebrated pi day at our school.

WONDERful, Vincent! How did your school celebrate? Thanks for WONDERing with us today!

Hello! Did you know that yesterday was pi day

You’re right, BreckyKristi! Do you know why it is called Pi Day? Have a WONDERful day!

Awesome this is super cool I’m just using a school iPad

That’s awesome, A! Technology is a WONDERful way to research and explore WONDERopolis! Check out Wonder #1054: How Does Your School Use Technology? and Wonder #710: How Does Technology Change Lives?. Thanks for commenting!