# Gaussian Integral and A Pi Approximator

I remember how I was happy when I find the integration of the Gaussian function in my high school years. It was an instantaneous spark which make me realize that increasing the integration dimension may bring a solution. Moreover, one can find a series expansion for Pi number after evaluating the integral.

#### Gaussian Integral

What is the Gaussian integral: Finding the area under the Gaussian function.$$I = \int_{-\infty}^{+\infty}\, e^{-\alpha x^2}\,dx$$