The Number π: The Number Whose Decimals Never End
Consider a simple circle.
If we divide the circumference of a circle by its diameter, we always obtain the same number:
π
This number is one of the most famous constants in the history of mathematics.
What Exactly Is π?
π is the ratio of a circle’s circumference to its diameter:
π = circumference ÷ diameter
Its approximate value is:
3.1415926535…
But the digits do not stop there.
Why Do the Digits of π Never End?
π is an irrational number.
This means that it cannot be expressed as the ratio of two integers.
As a result, its decimal expansion never terminates and does not settle into a repeating pattern.
If we continue writing the digits of π, we encounter an infinite sequence.
π Is More Than a Circle Constant
Because π comes from the geometry of a circle, it may seem that it is only useful for circular problems.
That is not true.
π appears throughout mathematics and science.
It can be found in geometry, trigonometry, calculus, physics, engineering, and many scientific equations.
Why Is Calculating π So Fascinating?
One reason π is fascinating is that calculating its digits has been a mathematical challenge for centuries.
Mathematicians throughout history have developed different methods for approximating π.
Today, computers can calculate an enormous number of digits.
However, most scientific and engineering applications require only a relatively small number of digits.
Can We Find the Last Digit of π?
No.
Because π is irrational, its decimal expansion continues forever.
Therefore, there is no “last digit” of π.
This may sound simple, but it is one of the most beautiful properties of the number.
One Number, One Huge Story
π shows us how a very simple concept can lead to deep mathematics.
The story begins with a circle:
circumference, diameter, and a ratio.
Yet this simple ratio appears across many areas of mathematics and science.
That is one reason π has become one of the most recognizable symbols in mathematics.