The trickiest of all these terms to understand is pi.
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…
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 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."
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."