Over 2.5 trillion decimal places!
pi news

I'd like to see them printed out.

I feel the urge to write the word

memorize

for no obvious reason.

/Tomas

Measure twice, cut once I always say.

That's a lot of pi!

Ron

Shucks. The previous record was 1.2 trillion digits. I had that down pat. Now I'm going to have to learn 1.3 trillion more!

I am still not worried - they are still as far as before from the last digit...

How does one calculate π?

I would drop needles on a tiled surface unless time was important to me.

Thomas Henry

only a Buffo(o)n would do something like that...

True. Real men calculate pi with frozen hot dogs.

Well! I've never been so offended in my life! I never would have thought my virility would be questioned on the Café, especially since I've never mentioned my book (ahem)...oops, I just did...

But I suppose we should offer some sort of serious response to Picard's original question. Buffon's needle approach will indeed offer up an approximation to Pi, but it converges extremely slowly and really isn't practical if you want a ton of digits in a reasonable amount of time.

A more accessible approach would be that of Archimedes. Inscribe and circumscribe polygons with a circle. These perimeters are easy to compute since they are rectilinear. Thus, one can trap the circumference of a circle within two bounds, and then Pi shakes out from this and the diameter. What's nice is that it only takes some geometry.

Or one could use a Taylor polynomial (a standard topic from Calculus II) which is perhaps more amenable to computer programs.

But in the final analysis (great pun, eh?) these computer results you hear about computing approximations to a bazillion places are using all sorts of tricks to speed up the convergence. It's part of a field known as numerical analysis.

So, Picard, it's not easy to answer your question briefly, but in a nutshell there are approaches using modeling, geometry, calculus and more advanced numerical analysis. The main difference among them is the efficiency of the computations.

Thomas Henry

I keep wondering how they know pi goes on forever without repeating if we haven't gotten to the end!

~Ben

http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
can be a bit hairy to follow if you're not into trigonometry or calculus.

Which will cause your spectators to pass out from boredom sooner; 8 perfect Faro shuffles in a row or reciting the digits of pi to 2.5 trillion decimals??

(I say the faro shuffles . . .)

If one could recite 5 digits per second, it would take over 15,000 years to recite 2.5 trillion decimal digits of pi.

I'd still take that over Sam the Bellhop.

Hahahahaha