Pi

π is the ratio of the circle's circumference to its diameter, commonly approximated as 3.14159.

Pi is the ratio of the circle's circumference to its diameter, commonly approximated as 3.14159.

Pi is often written as the Greek letter π. Pi is an irrational number, meaning it cannot be written as the normal fraction ($a \over b$), but π can be represented by an infinite series of fractions, also known as the continued fraction:

$\pi =3+\textstyle {\frac {1}{7+\textstyle {\frac {1}{15+\textstyle {\frac {1}{1+\textstyle {\frac {1}{292+\textstyle {\frac {1}{1+\textstyle {\frac {1}{1+\textstyle {\frac {1}{1+\ddots }}}}}}}}}}}}}}$

However, it is very useful in many ways, not just measuring circles.

Mathematicians have known about π for thousands of years.

There are different sequences that approximate π. Taking 22/7, has an error of about 0.04%. This is sufficient for many applications.

Leibniz' formula for π, due to Gottfried Leibniz, states that

$\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots ={\frac {\pi }{4}}.$