A Brief History of PI

A Brief History of π ("pi")

The ratio of the circumference to the
diameter of a circle is constant (namely, pi) has
been known for almost 4000 years.

Pi has been calculated to over one trillion
digits beyond its decimal point. As an irrational
and transcendental number, it will continue
infinitely without repetition or pattern.

The ancient Babylonians generally
calculated the area of a circle by taking 3 times
the square of its radius ( =3).

The ancient Babylonians calculated the area of a circle by
taking 3 times the square of its radius, which gave a value of
pi = 3.

But one Old Babylonian tablet (from ca. 1900-
1680 BCE) indicates a value of 3.125 for pi.

The ancient Babylonian tablet

The Rhind Papyrus (ca.1650 BC) gives us
insight into the mathematics of ancient Egypt.
The Egyptians calculated the area of a circle by

a formula that gave the approximate value of
3.1605 for pi.

Rhind Papyrus

The first theoretical calculation of a value of
pi was that of Archimedes of Syracuse (287-
212 BC), one of the most brilliant
mathematicians of the ancient world.

Archimedes calculate pi’s value by using
the help of polygons. Essentially, he computed
upper and lower bounds of pi, by drawing a
hexagon inside and outside of a circle. Then
doubled the number until reaching a 96-sided

polygon. By doing this, he proved that pi
equaled 223/71 < π < 22/7 and/or (3.1408 < π
< 3.1429).

Archimedes

Zu Chongzhi

Zu Chongzhi (429–501), a brilliant Chinese
mathematician and astronomer, calculated pi
equaled around 355/133 by using Hui’s
algorithm, applying it to a 12,288 sided polygon.
With a correct assumption of the first 7 digits of
pi in the form of “3.141592920” remained the
most accurate approximation of pi for the next
800 plus/minus years to come.

Mathematicians began using the Greek
letter π in the 1700s .The symbol of pi was
introduced by the British mathematician William
Jones in 1706, who wrote: = 3.14159.

William Jones

This symbol was adopted by Euler in 1737
and became the standard symbol for pi.

Leonhard Euler