## A Much Bigger Piece Of Pi 729

Posted
by
timothy

from the mmmm-pi dept.

from the mmmm-pi dept.

Punk_Rock_Johnny points to an AP story on Pi-obsessed Professor Yasumasa Kanada. A snippet from the story:

*"Kanada and a team of researchers set a new world record by calculating the value of pi to 1.24 trillion places, project team member Makoto Kudo said yesterday. The previous record, set by Kanada in 1999, was 206.158 billion places."*Trillion! "
## One simple question (Score:2, Insightful)

## Re:One simple question (Score:1, Insightful)

## Re:OK, now this is overkill (Score:4, Insightful)

size of the proton: ~ 1 fm = 10^-15 m

age of the universe: ~15 Gyr

speed of expansion ~ c = 3 x 10^8 m/s

gives:

proton/cosmic radius ~ 10^-42

So you need about 40 places for this. Of course, you might want to calculated it to the Plank scale, so maybe tack on a few more.. say 100 for safety. Yes, a trillion digits does seem a bit like overkill.

## why? (Score:1, Insightful)

## Re:One simple question (Score:2, Insightful)

## Re:Signature of God? (Score:5, Insightful)

anyfinite sequence appears somewhere along the expansion of the number. So trivially, that image of a circle is in there somewhere, as is an image of a triangle, the source to Linux 4.0, an image of Bush playing with G.I. Joe dolls on his desk and so on.## Re:Well ... what is it? (Score:5, Insightful)

Usually, "X compresses down to one bit for a correct algorithm" is a snarky answer, but in this case, it actually makes sense. Generally one has to define those algorithms as a table, where "X" is what the decompression function returns for "1", which definately feels like cheating. In this case, though, one can provide a finite algorithm to compute as many digits of pi as you please, so it makes sense.

In fact, we compress pi down to one or two bytes, with a mathematically defined decompression sequence you can use if you want, all the time. In fact, I've done it three times in this post already, where two different two byte sequences stood in for the infinite series that is that number. Can you find them?

## Re:Signature of God? Probably not (Score:2, Insightful)

Your assertion that pi is the same in all possible universes seems quite silly to me. ... because everythin on the basis of which we conceive of that is part and parcel of the universe itself, including the laws of physics.Sorry, you're dead wrong here. First, pi and circles have nothing to do with physics. There are no circles (as mathematicians define them) in our universe. Pi is an abstract concept, not a physical object. We can conceive of them nonetheless. The human mind is hardly limited by the physics of our universe. Suggesting that it is is, well, silly, and flatly contradicted by watching an hour or so of Saturday-morning cartoons. I can conceive of things that don't exist in our universe, and so can you.

It's possible that another intelligent species might not conceive of pi. But any that do will come up with the same value (though they may represent it in a different base). Or they may use circumference / radius, giving a value of 2*pi, but that doesn't affect the discussion.

Pi's value is what it is. It has nothing to do with anything in any physical reality. It's a pure mathematical concept, and as such, will have the same value for anyone who conceives of it.

This is really no different that observing that 1 and 2 have the same value in all possible universes. You may name and write them differently, but that doesn't affect their values. Pi is merely another (somewhat more compicated) number. Not even a god can change its value. They can define another value, but it won't be pi.

--

## Better Approximation (Score:2, Insightful)

This differs from the true value 3.14159265358979 by less than 0.00001% while 22/7 has an error of 0.04%.

It is also easy to remember:

start with 113355 (first three odd digits repeated)

break it up with a / : 113/355 and

invert 355/113

## Re:One simple question (Score:2, Insightful)