TITLE: Is there a real number lookup algorithm or service?
QUESTION [22 upvotes]: 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. $\displaystyle\frac{\pi^2}{6}$) 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 $\displaystyle\sum_{n=1}^\infty \frac{1}{n^2}$, look up the answer ("looks close to $\displaystyle\frac{\pi^2}{6}$") and then use the likely answer to help find a proof that the sum really is $\displaystyle \frac{\pi^2}{6}$.
Does such a thing exist?

REPLY [25 votes]: I've long used Simon Plouffe's inverse symbolic calculator for this purpose.  It is essentially a searchable list of "interesting" numbers.
Edit: link updated (Mar 2022).