What is gained by computing additional digits of $\pi$? 
Possible Duplicate:
Do We Need the Digits of $\pi$? 

Given that at 39 digits, we have enough of $\pi$ to calculate the volume of the known universe with (literally!) atomic precision, what value is gained? Are there other formulas for which more digits of $\pi$ are useful? If so how many digits of $\pi$ do we need before there's no gain?
 A: The practicality of knowing $\pi$ to so many digits has long since passed.  I think the main reason people continue to calculate its digits is because there is a certain prestige that goes along with being able to calculate more digits than anyone else.  It brings notoriety, especially when testing a new supercomputer.
A: There is no practical gain in computing the circumference of a physical circle. As a matter of fact, most exercises in computing more and more digits of $\pi$ are rather some kind of computer benchmark tests (or may in fct detect computer malfunction to some extent).
In theory, it is at least feasible that a rather good approximation of $\pi$ might be needed for some intricate proof (say, of the Riemann hypothesis), but to repeat it: That would not be related to physical circle circumferences.
A: The hunt for more digits of $\pi$ helps to spur research into analysis, especially in developing new methods for accelerating convergence of sums.  See, for instance, Bailey-Borwein-Plouffe.
A: As per  wikipedia: Pi

For most numerical calculations involving π, a handful of digits provide sufficient precision. According to Jörg Arndt and Christoph Haenel, [as you point out,] thirty-nine digits are sufficient to perform most cosmological calculations, because that is the accuracy necessary to calculate the volume of the known universe with a precision of one atom.

Despite this, people have worked strenuously to compute $\pi$ to thousands and millions of digits. This effort may be partly ascribed to the human compulsion to break records, and such achievements with $\pi$ often make headlines around the world. 
(This obsession with/compulsion to memorize/calculate more and more of the digits of $\pi$, may also, for at least a few, constitute a manifestation of OCD, and provide grounds for such a diagnosis!)
(To the credit of $\pi$ and its digits) They do have practical benefit:

... such as testing supercomputers, testing numerical analysis algorithms (including high-precision multiplication algorithms); and within pure mathematics itself, providing data for evaluating the randomness of the digits of π.

...[and can be applied to test the accuracy and]

...the "global integrity" of a supercomputer. A large scale
  calculation of pi is entirely unforgiving; it soaks into all parts of
  the machine and a single bit awry leaves detectable consequences.

A: I could see it to be useful to gain insight on some of $\pi$'s properties. For example, we don't know whether $\pi$ is normal or not (normal number is 'morally' a number where each digit is equiprobable in every base), so a statistical analysis of known digits may hint at that (that would not prove it, obviously).
A: $\pi$ is also used to randomly generate numbers. Maybe there are some applications there too.
π as a random number generator
