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It’s that time of the year again, Wonder Friends! Time to celebrate Pi Day on March 14th!

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=πr2 — 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.”

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    • 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®! :-)

    • 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? :-)

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

  1. 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! :-)

    • 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! :)

  2. 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! :-)

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

    • 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! :-)

  3. 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! :-)

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Have you ever wondered…

  • What is pi?
  • What is an irrational number?
  • What is the final digit of pi?

Wonder Gallery

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Try It Out

Ready to celebrate the mathematical WONDER that is pi? Grab 3 or 14 friends and family members to help you explore the following activities:

  • The mathematical constant pi (π) has fascinated mathematicians and non-mathematicians alike for thousands of years. With the supercomputers we have today, playing around with pi is even easier and more fun. Log on, head to the Internet and check out these interesting pi-related sites:
  • Is pi really a constant? Don’t take mathematicians’ word for it! Find out for yourself. Grab a few circular objects and a ruler or tape measure. For each of these circular objects, measure the circumference and diameter and then divide the circumference by the diameter. What answer do you get? Isn’t it interesting how the ratio of these two measurements is constant even though the size of the circles changes?
  • By far the best way to celebrate Pi Day is by eating pie. After all, pies are round. But more importantly, they’re filled with delicious flavor. Check out the recipes below and choose one to make at home. And before you go thinking that it’s weird to celebrate a mathematical holiday by cooking, just remember that there’s going to be plenty of math involved in measuring ingredients, calculating temperatures, and precisely timing the cooking. Enjoy your Pi Day!

Still Wondering

How do the area and circumference of a circle compare to its radius and diameter? Find out by exploring Illuminations’ fun, interactive Circle Tool lesson!


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