## 26 March 2017

### Pi

The number $\pi$ is a constant equal to the ratio of the perimeter of a circle and its diameter, and it is approximately equal to $3.14159$. In the middle of $18$th century it was represented by the Greek letter $\pi$. Pi is an irrational number, i.e., can not be expressed exactly as a ratio of two integers. However, some fractional numbers represent good approximations of $\pi$, as Aryabhata has discovered.

Curiosities:

$\pi \approx \frac{22}{7}$

$\pi = \frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}+ \cdots$

The circumference of a circle of radius $r$ is $2\pi r$.

The area of a circle of radius $r$ is $\pi r^2$.

The volume of a sphere of radius $r$ is $\frac{4}{3}\pi r^3$.

The surface area of a sphere of radius $r$ is $4\pi r^2$.

$2\pi$is the period of the sine and cosine and $\pi$ is the period of the tangent.

$e^{i\pi}+1=0$ (Euler's identity).

Every year, on March $14$ ($3/14$ in the month/day format), we celebrate the Pi Day!