## Pages

### Pi day

$\pi$ day is celebrated every year on March 14 because $\pi \approx 3.14$.

The number $\pi$ is ultimately associated with the circle. By definition, if we draw a circle of radius 1, then $\pi$ is the length of a semicircle.

In the figure below, if we go from A $\to$ B $\to$ C $\to$ D by straight lines then the length of the trip is 3, but if we go by the circle then the trip length is $\pi$,

so $\pi$ is a tiny bit bigger than 3:
$$\pi > \approx 3$$

There is an easy way to remember the decimal value of $\pi$. First, we write the three pairs of odd numbers as follows
$$11~33~55$$

Now cut the above number into two halves
$$113~~\mid~~355$$

If we take the bigger number divide by the smaller number, we will have
$$\frac{355}{113} = {\bf 3.141592}~92...$$
Whereas, $$\pi= {\bf 3.141592}~65...$$
So with this method, $\frac{355}{113}$, we can derive and remember the first 6 decimal digits of $\pi$.

To celebrate this year's $\pi$ day, let us enjoy this beautiful identity due to the mathematician Viete:
$$\frac{2}{\pi} = \sqrt{\frac{1}{2}} \cdot \sqrt{\frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}} \cdot \sqrt{\frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}}} \cdots$$
Happy $\pi$ day everyone!!!