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 among 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. That’s 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 more than 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: 3.1415926535897932384626433832795028841971693993751 058209749445923078164062862089986280348253421170679
• Pi to 1000 digits: 3.141592653589793238462643383279502884197169399375
  105820974944592307816406286208998628034825342117067982148086513
  282306647093844609550582231725359408128481117450284102701938521
  1055596446229489549303819644288109756659334461284756482337867831
  6527120190914564856692346034861045432664821339360726024914127372
  4587006606315588174881520920962829254091715364367892590360011330
  53054882046652138414695194151160943305727036575959195309218611738
  19326117931051185480744623799627495673518857527248912279381830119
  4912983367336244065664308602139494639522473719070217986094370277
  0539217176293176752384674818467669405132000568127145263560827785
  7713427577896091736371787214684409012249534301465495853710507922
  79689258923542019956112129021960864034418159813629774771309960518
  70721134999999837297804995105973173281609631859502445945534690830
  26425223082533446850352619311881710100031378387528865875332083814
  20617177669147303598253490428755468731159562863882353787593751957
  7818577805321712268066130019278766111959092164201989

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.