Hatrack River Forum: Did I do this right?

This is topic Did I do this right? in forum Books, Films, Food and Culture at Hatrack River Forum.

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Posted by kaioshin00 (Member # 3740) on :

I was bored, so I've tried to prove the area of circle is pi r^2. I know it would be easy to use integration to prove this, so I tried a different method:

Here

Did I do it right?

Posted by Tatiana (Member # 6776) on :

Very cool! What else can we prove?

Posted by Mike (Member # 55) on :

How about a proof of

1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = (pi^2)/6

?

Posted by kaioshin00 (Member # 3740) on :

Hello Taylor series

Posted by kaioshin00 (Member # 3740) on :

Ok..so i guess it's right.

Posted by Hobbes (Member # 433) on :

Yah you did, and I guess techincally you didn't use integration, but that was polar integration only you didn't get to use any of the tricks that make it easier. [Razz]

Cool though, what did you use to make the graphics?

Hobbes [Smile]

Posted by kaioshin00 (Member # 3740) on :

I refuse to use integration! [Wink]

And I made it in Photoshop CS.

Posted by Hobbes (Member # 433) on :

quote:
How about a proof of

1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = (pi^2)/6

This would be a proof of a special case of the Riemann Zeta function, which is used by super-computers to find subsequent digits of pi. A proof of this special case can be found here.

This function is also useful in determining primes, and a Purdue proffesor (my school [Smile]

) claims he's solved something called the "Riemann Hypothesis", which is basically that the zeros for the Riemann Zeta function (sum (1/n)^x n0->inf) in the complex plane are all contained on the vertical line going through real part = 1/2.

We'll see if his proof is accepted, most people don't seem to beleive him, but he's solved a biggie before so who knows.

Hobbes [Smile]

Posted by Tatiana (Member # 6776) on :

I like Euclid's proof of the infinitude of the primes. This one is not mine, I cribbed it from a dead Greek guy.

Assume there is a largest prime number, call it P. (A prime number, for you nonmathgeeks, is any integer greater than 1 which is not evenly divisible by any other integer besides itself and 1.)

Make the number P! + 1 and call it N.
(P factorial is just P * (P-1) * (P-2) * ... * 3 * 2 * 1. For example, 6! is 6*5*4*3*2*1 = 720.)

N isn't divisible by 2 because there's one left over when you divide it by 2. (Since P! IS divisible by 2, then P! + 1 can't be.)

Similarly, N isn't divisible by 3, nor by 4, nor by any number up to and including P.

Therefore, either N is prime itself, or else it's divisible by a prime bigger than P.

Therefore the supposition that P is the largest prime must be wrong.

Therefore there can be no largest prime.

[ October 31, 2004, 01:35 PM: Message edited by: Tatiana ]

Posted by Verily the Younger (Member # 6705) on :

I never understood them folks as say that pi r^2. Far as I can tell, pie are round. [Confused]

Posted by BunnV (Member # 6816) on :

[Group Hug]

<--what is the area of this hug?

Posted by Tatiana (Member # 6776) on :

That's not a hug, that's the post apocalyptic mutants huddled around a nuclear waste dump.

Posted by Da_Goat (Member # 5529) on :

Couldn't it be post-apocalyptic mutants hugging around a nuclear waste dump? Or do you think mutants are incapable of love? Didn't X-Men teach you anything? [Frown]

[ November 02, 2004, 01:36 AM: Message edited by: Da_Goat ]

Posted by BunnV (Member # 6816) on :

lol, i think anyone who managed to live in the post apocalyptic era should all be friends. That'd be HUGe.

Posted by kaioshin00 (Member # 3740) on :

Yeah, it seems like they've really embraced the new post-apocalyptic earth [Wink]