Converting Pi to binary: Don't do it!

[Triple Zero]

http://everything2.com/title/Converting+Pi+to+binary%253A+Don%2527t+do+it%2521

WARNING: Do NOT calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains ALL finite bit strings.

If you compute it, you will be guilty of:
Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code)
Trademark infringement
Possession of child pornography
Espionage (unauthorized possession of top secret information)
Possession of DVD-cracking software
Possession of threats to the President
Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords
Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie.
Defaming Scientology. Which IS illegal -- just ask Keith Henson.
Also, your computer will contain all of the nastiest known computer viruses. In fact, all of the nastiest possible computer viruses.

Some of the files on my PC are intensely personal, and I for one don't want you snooping through a copy of them.

You might get away with computing just a few digits, but why risk it? There's no telling how far into Pi you can go without finding the secret documents about the JFK assassination, a photograph of your neighbor's six year old daughter doing the nasty with the family dog, or a complete copy of the not-yet-released Star wars movie. So just don't do it.

The same warning applies to e, the square root of 2, Euler's constant, Phi, the cosine of any non-zero algebraic number, and the vast majority of all other real numbers.

There's a reason why these numbers are always computed and shown in decimal, after all.

[Don Coyote]

Binary is the language of the -o-s.

[Richter]

I accidentally to 1120 decimal places.   

[Telarus]

 


Hey, have you all seen this: http://tauday.com/

[Requia ☣]

I really wish I still had math professors to troll with that.

[AFK]

What happens if after that you divide by zero? 

[Jasper]

Hey, have you all seen this: http://tauday.com/

That was cool.

[Triple Zero]

It is. I was already familiar with it.

The Tau thing, and the fact that you need only 50 (or so) digits of pi in order to calculate the circumference of the observable universe to the precision of a proton, is pretty much all you need to know about pi.

[rong]

I'm aware the OP says any finite string of numbers will show up
in the digits of Pi (or whatever irrational number you choose).  But, I think,
using induction, one can prove that even an infinite string will also show up.

***** for the "lighter" version, skip to the next "******"

what i'm getting at is, i think it can be shown that if you go out far enough
in the digits of Pi, you will eventually find the exact digits of, say, e.

(for the sake of discussion, i'm using Pi and e, but the same argument can be
made for any pair of irrational numbers)

we certainly would agree that for any N digits of e, you should find a string
somewhere in the digits of Pi that is exactly those digits. I'm not 100% sure,
but i think you can use induction (or something similar) to say that since it is
true for any N, it is true for N = infinity.

(just a heads up - the N in the preceeding paragraph is not the same as the N in
the following paragraph)

in other words, if Pi = [pn,pr] where pn = "the first N digits of Pi" and
pr = "the rest of the digits of Pi" then it can be shown that there
exists some N such that pr = "the digits of e"

if we think of numbers Pn and Pr where Pn = 3.14159 . . . (out to N digits) and
Pr = 0.00000 . . . 271828183 (N zeroes followed by the digits of e)

then we know that Pn is a rational number (any finite decimal is rational) and
we have a number Pr that is simply e with the decimal place slid to the left, or
a multiple of e.

we have Pi = Pn + Pr and Pn = k*e 

or Pi = k*e + Pr  where k and Pr are both rational numbers. 



*****

i think it can be shown that Pi = A*e + B
where A and B are rational numbers.

I can't for the life of me figure out the best way to go about finding A and B, though.

but, finding A and B would prove that somewhere in the digits of Pi is (are?)
the digits of e. (and vice versa)


aside:

does anyone know if 0.1234567891011121314151617181920212223242526272829303132. . .
is an irrational number?

[Igor]

But if you can fit one infinite number (e) into the digits of pi, shouldn't you be able to fit all infinite numbers?

And isn't that impossible?

[Nawaxo]

If you can find one infinite string how can you fit a second one?  If you were to have two infinite numbers, then you need to have the first digits of both of them. One will have to appear before the other one, so the first string will have to end. By induction you can only say that, given any finite sequence of digits from an infinite (or finite) number, they are bound to appear if the conjecture is true.

[Triple Zero]

aside:

does anyone know if 0.1234567891011121314151617181920212223242526272829303132. . .
is an irrational number?

Yes it is. I forgot why,  but it wasnt that complicated so I bet you can figure it out.

[LaughingOtter]

It's the base 10 representation of the Champernowe constant. It's a non-terminating, non-repeating number, so it's transcendant and therefore irrational.

[Akara]

I sent both of these websites to my PhD in math candidate mother. I think she's stopped talking to me now. lol

[Requia ☣]

But if you can fit one infinite number (e) into the digits of pi, shouldn't you be able to fit all infinite numbers?

And isn't that impossible?

Infinity does not necessarily equal infinity, so I wouldn't qualify it as impossible.