Author Topic: A challenge to all recreational mathematicians  (Read 6045 times)

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Offline Petrarch of the VBB

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A challenge to all recreational mathematicians
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!

 

Offline CP5670

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A challenge to all recreational mathematicians
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. :p :D

Here are a couple I can think of that will use up less time and webspace: :D (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 × ( ep + e-p )

3: If y=xxxx..., prove that x=y1/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. ;7
« Last Edit: November 05, 2002, 02:24:09 pm by 296 »

 

Offline Ulundel

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A challenge to all recreational mathematicians
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.

 

Offline ZylonBane

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Re: A challenge to all recreational mathematicians
Quote
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!
ZylonBane's opinions do not represent those of the management.

 

Offline Joey_21

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A challenge to all recreational mathematicians
Quote
Originally posted by CP5670

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


:lol:

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. :p

Quote
Originally posted by CP5670

2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( ep + 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? :confused:
« Last Edit: November 05, 2002, 03:47:27 pm by 34 »

 

Offline Razor

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A challenge to all recreational mathematicians
Quote
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 × ( ep + e-p )

3: If y=xxxx..., prove that x=y1/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. :yes:

 

Offline Sandwich

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Offline Thor

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A challenge to all recreational mathematicians
Prove the meaning of life mathmatically.
I can't believe my profile is still active... member since  July 25, 2002

 

Offline Goober5000

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A challenge to all recreational mathematicians
e^(i*pi)+1=0, QED. :D

 

Offline HotSnoJ

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A challenge to all recreational mathematicians
Quote
Originally posted by Thor
Prove the meaning of life mathmatically.


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

*hides and puts on flame retardant clothes*
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Offline CP5670

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A challenge to all recreational mathematicians
Quote
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. :p (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)

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


there you go... ;7

Quote
"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. :D

Quote

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. :p


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. :D (there is one for the Stieltjes constants that takes some 50 million terms to get one digit of accuracy. :rolleyes: )

Quote
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? :confused:


Yep, that's where that term comes from in this case. :D (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).

Quote
Prove the meaning of life mathmatically.


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

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

 

Offline an0n

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A challenge to all recreational mathematicians
I now sacrifice myself on the alter of bad humour in the hopes of saving all who come after me:

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Offline Bobboau

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A challenge to all recreational mathematicians
"deatomizing the entire universe to write down a simple number"
I think I've found CP's purpose of exsistance
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Offline Sandwich

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A challenge to all recreational mathematicians
Quote
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... ;)
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"...The quintessential quality of our age is that of dreams coming true. Just think of it. For centuries we have dreamt of flying; recently we made that come true: we have always hankered for speed; now we have speeds greater than we can stand: we wanted to speak to far parts of the Earth; we can: we wanted to explore the sea bottom; we have: and so  on, and so on: and, too, we wanted the power to smash our enemies utterly; we have it. If we had truly wanted peace, we should have had that as well. But true peace has never been one of the genuine dreams - we have got little further than preaching against war in order to appease our consciences. The truly wishful dreams, the many-minded dreams are now irresistible - they become facts." - 'The Outward Urge' by John Wyndham

"The very essence of tolerance rests on the fact that we have to be intolerant of intolerance. Stretching right back to Kant, through the Frankfurt School and up to today, liberalism means that we can do anything we like as long as we don't hurt others. This means that if we are tolerant of others' intolerance - especially when that intolerance is a call for genocide - then all we are doing is allowing that intolerance to flourish, and allowing the violence that will spring from that intolerance to continue unabated." - Bren Carlill

 

Offline Goober5000

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

 

Offline mikhael

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A challenge to all recreational mathematicians
Quote
Originally posted by Goober5000
e^(i*pi)+1=0, QED. :D


Now THAT is beauty. :D
[I am not really here. This post is entirely a figment of your imagination.]

 

Offline CP5670

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A challenge to all recreational mathematicians
That result is possibly the most beautiful in all of mathematics. :D :nod:

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.

 

Offline Goober5000

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A challenge to all recreational mathematicians
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?
« Last Edit: November 06, 2002, 10:20:06 pm by 561 »

 

Offline Joey_21

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A challenge to all recreational mathematicians
Quote
Originally posted by CP5670
2: Prove the following:
(1+1/1²)×(1+1/2²)×(1+1/3²)×(1+1/4²)... = 1/p × ( ep + 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? :wtf:

 

Offline Killfrenzy

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A challenge to all recreational mathematicians
*Looks at this entire thread, then throws up*
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