What's an intuitive explanation of the following mathematical fact:[math]\displaystyle \sum_{n=1}^{\infty}{\frac{1}{n^2}} = \frac{\pi^2}{6}[/math]?
How do I intuitively understand [math]\int_ {0} ^ {\infty} e^ {-x^2} dx = \Gamma (\frac {3} {2}) = \frac {1} {2}! = \frac {\sqrt {\pi}} {2}[/math]?