Is there a way of taking a number known to limited precision (e.g. 1.644934) and finding out an "interesting" real number (e.g. $pi^2/6$) that's close to it?

I'm thinking of something like Sloane's Online Encyclopedia of Integer Sequences, only for real numbers.

The intended use would be: write a program to calculate an approximation to $sum_{i=0}^\infty 1/n^2$, look up the answer ("looks close to $pi^2/6$") and then use the likely answer to help find a proof that the sum really is $pi^2/6$.

Does such a thing exist?