Pi

Pi, written as π, is a universally recognized mathematical constant that is irrational, for it neither repeats nor terminates.

Below is what a ninth-grade geometry student memorizes of pi.


 * $$\pi\, = 3.141592653589793238462643383279502884197...$$

Below is the first 100 digits of pi.


 * $$\pi\, = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...$$

Mathematicians all over the world are continuing to find out the mystery of pi to this day. Though recent computations churn out 1 trillion decimals of pi, scientists only need a few hundred. Nevertheless, the record for the most digits of pi memorized, as of 2012, are 65,000.

Attempts To Find Pi
Scientists have been trying to form an equation that precisely equals pi for centuries, even though pi is a transcendental number; it cannot be equated with a formula.

Below are a number of ways mathematicians dating back to the 1700s have attempted to reach pi with a formula.


 * $$\frac{22}{7}\, > \pi\,$$


 * $$\int_{-1}^1\,\sqrt{1-x^2}\,dx = \frac{\pi\,}{2}\,$$


 * $$\frac{2}{\pi\,}\, = \frac{\sqrt{2}\,}{2}\, * \frac{\sqrt{2+{\sqrt{2}\,}}\,}{2}\, * \frac{\sqrt{2+{\sqrt{2+{\sqrt{2}\,}}\,}}\,}{2}\,...$$


 * $$\pi\, \approx\, \frac{2nl}{xt}\,$$


 * $$\pi\, = \frac{C}{d}\,$$

Pi Day
Pi Day is an international holiday celebrated every March 14, in correspondence to the first three digits of pi.

Other Uses of π
A capital π is used in product notation as a large operator.

E.g.


 * $$\prod_{x=1}^{10}x = 10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 3628800$$

In geometry and algebra, π is also used to measure radians.