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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!!!



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