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Pi day






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


If we draw a circle of radius 1, then $\pi$ is the length of a semicircle.

The length of the whole circle is denoted by $\tau$, thus, $$\tau = 2 \pi \approx 6.28$$


In the figure below, the perimeter of the hexagon is 6, so the circumference of the circle is a little bit greater than 6:
$$\tau > \approx 6$$
so $\pi$ is a tiny bit bigger than 3:
$$\pi > \approx 3$$




To celebrate this year's $\pi$ day, let us enjoy this beautiful identity about $\pi$ due to the mathematician Euler:
$$\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \dots = \frac{\pi^2}{6}$$

Happy $\pi$ day everyone!!!





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