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

Now cut the above number into two halves

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!!!

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