There are many interesting formulae in mathematics;
must be one of the most amazing of all.
The first reaction is where did that come from? You can find 14 different proofs of this in a paper on Robin Chapman’s Home Page [look for Evaluating zeta(2)]
Given this result can you prove another amazing result?
If you pick two positive integers at random, the probability of them having no common divisor is
gets everywhere! See Wikipedia for more such as
- or or