26 March 2017

Pi


The number \(\pi\) is a constant equal to the ratio of the perimeter of a circle and its diameter, and it is approximately equal to \(3.14159\). In the middle of \(18\)th century it was represented by the Greek letter \(\pi\). Pi is an irrational number, i.e., can not be expressed exactly as a ratio of two integers. However, some fractional numbers represent good approximations of \(\pi\), as Aryabhata has discovered.

Curiosities:

\(\pi \approx \frac{22}{7}\)

\(\pi = \frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}+ \cdots\)

The circumference of a circle of radius \(r\) is \(2\pi r\).

The area of a circle of radius \(r\) is \(\pi r^2\).

The volume of a sphere of radius \(r\) is \(\frac{4}{3}\pi r^3\).

The surface area of a sphere of radius \(r\) is \(4\pi r^2\).

 \(2\pi\)is the period of the sine and cosine and \(\pi\) is the period of the tangent.

 \(e^{i\pi}+1=0\) (Euler's identity).

Every year, on March \(14\) (\(3/14\) in the month/day format), we celebrate the Pi Day!

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