[Petrarch of the VBB]

For those of you with an unhealthy interest in maths (this means you, CP) i have a challenge, try and write Graham's number using conventional methods.
For those of you who dont know what graham's number is, here is a summarized description, the number 3^^^...^^^3 in which there are 3^^^^3 arrows, then take that number and make that the number of arrows, reapeat 63 times!

[CP5670]

It is theoretically possible to do this using the usual exponents since 3 is an integer but the problem is that I could use up all the webspace Gamespy has (and all the time in my life) in writing a huge post and only get a very small fraction of the required number.

Here are a couple I can think of that will use up less time and webspace: (the dots indicate that it goes on forever)

1: Prove the following:
z(2) = 1/1²+1/2²+1/3²+1/4²... = p²/6

2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( e^p + e^-p )

3: If y=x^xxx..., prove that x=y^1/y for convergent values of x. (or in terms of y, y = - plog( - log(x) ) / log(x) )

now this is what math is all about.

[Ulundel]

CP please explain me how a line of jibba-jabba can be better than hangin around with people, getting drunk, and having sex. mmh? give me one good reason.

*makes yoda face*

but it's actually nice too...in its own way.

[ZylonBane]

Originally posted by Petrarch of th VBB
try and write Graham's number using conventional methods.

"Graham's number cannot be expressed using the conventional notation of powers"

Ha!

[Joey_21]

Originally posted by CP5670

1: Prove the following:
z(2) = 1/1²+1/2²+1/3²+1/4²... = p²/6

I wrote a java program using a loop to test this out and then multipled it by 6 and took the square root of it to get pi.

where the formula goes:
From 1 to 1000000 the loop used x^-2 and added it to itself 1000000 times. The end result was 3.1415916986605086 (which is only accurate up to 5 places behind the decimal). This thing converges fricken slow! I prefer to use the inverse sine series to generate pi... lots faster.

Originally posted by CP5670

2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( e^p + e^-p )

btw... that looks a bit like the formula for hyperbolic cosine (where Cosh(x) = (e^x+e^-x)/2)... I've always wondered, what is the purpose of the hyperbolic functions anyway?

[Razor]

Originally posted by CP5670


1: Prove the following:
z(2) = 1/1²+1/2²+1/3²+1/4²... = p²/6

2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( e^p + e^-p )

3: If y=x^xxx..., prove that x=y^1/y for convergent values of x. (or in terms of y, y = - plog( - log(x) ) / log(x) )
 

How we say it in good ol' YU,....the same to you.

[Sandwich]

Originally posted by ZylonBane
"Graham's number cannot be expressed using the conventional notation of powers"

Ha!

Bah! From the Department of Don't-Believe-Everything-You-Read Department.

[Thor]

Prove the meaning of life mathmatically.

[Goober5000]

e^(i*pi)+1=0, QED.

[HotSnoJ]

Originally posted by Thor
Prove the meaning of life mathmatically.

lets see mister CP meet that challenge. But everyody knows thats impossible.

*hides and puts on flame retardant clothes*

[CP5670]

CP please explain me how a line of jibba-jabba can be better than hangin around with people, getting drunk, and having sex. mmh? give me one good reason.

*makes yoda face*

actually even if it was just "jibba-jabba," it would still be much better than the other stuff. (people in general are pretty boring unless you are talking about math, computer games or legos while the other two activities are equivalent to smashing your head against a wall)

but it's actually nice too...in its own way.

there you go...

"Graham's number cannot be expressed using the conventional notation of powers"
Ha!

I guess that is because there is not enough ink in the universe, but it is still possible in theory.

I wrote a java program using a loop to test this out and then multipled it by 6 and took the square root of it to get pi.

where the formula goes:
From 1 to 1000000 the loop used x^-2 and added it to itself 1000000 times. The end result was 3.1415916986605086 (which is only accurate up to 5 places behind the decimal). This thing converges fricken slow! I prefer to use the inverse sine series to generate pi... lots faster.

lol yeah this formula is no good for numerically computing pi, but it is actually one of the better converging sums I have seen out there. (there is one for the Stieltjes constants that takes some 50 million terms to get one digit of accuracy. )

btw... that looks a bit like the formula for hyperbolic cosine (where Cosh(x) = (e^x+e^-x)/2)... I've always wondered, what is the purpose of the hyperbolic functions anyway?

Yep, that's where that term comes from in this case. (this can be seen by evaluating and simplifying the product using gamma functions) I guess those are basically just real versions of the circular trig functions and have their own notation only because they come up often (same goes for the circular functions).

Prove the meaning of life mathmatically.

Here is one way of putting it:
sin( x³ )=0

(in other words, life has an infinite number of meanings, but not all possible meanings)

[an0n]

I now sacrifice myself on the alter of bad humour in the hopes of saving all who come after me:

42

*dies*

[Bobboau]

"deatomizing the entire universe to write down a simple number"
I think I've found CP's purpose of exsistance

[Sandwich]

Originally posted by Bobboau
"deatomizing the entire universe to write down a simple number"
I think I've found CP's purpose of exsistance

Heh - I was beginning to wonder if anyone read that page...

[Goober5000]

I read it.  Heavy stuff.  I'm still not sure I completely understand ^^^^^ notation.

[mikhael]

Originally posted by Goober5000
e^(i*pi)+1=0, QED.

Now THAT is beauty.

[CP5670]

That result is possibly the most beautiful in all of mathematics.

Here are some other neat ones:



And then there is also Khinchin's law for continued fractions, which is one of the most astounding things I have ever seen, but I don't know enough about that field to be able to prove it.

[Goober5000]

I think that e^(i*pi)+1=0 is God's signature on the mathematical continuum of the universe.

Some of us less enlightened (but no less interested in mathematics) haven't heard of some of these things.  Links are A-1 SUPAR. For example, what is G, the gamma function, the beta function, and Khinchin's Law?

On that note, thanks for describing K(x). What is it used for?

[Joey_21]

Originally posted by CP5670
2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( e^p + e^-p )

I have to disagree with this. I went to term 10000000 in the generation of this series and I ended up with 3.6760775427785917... whereas (e^pi+e^-pi)/pi = 7.37966665555814939701766565277332......

Are you sure you have the series correct?

[Killfrenzy]

*Looks at this entire thread, then throws up*