U NEED TO SEE THIS!!!!!!

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Re: U NEED TO SEE THIS!!!!!!

Postby Silverdream » Sun Sep 29, 2013 7:58 pm

Image

Now open wide.
Image

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Re: U NEED TO SEE THIS!!!!!!

Postby samuelzz10 » Sun Sep 29, 2013 8:09 pm

Silverdream wrote:Image

Now open wide.

Nah, I don't feel too stiff anymore.

I am excited about the new Joan Jett album though.
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Re: U NEED TO SEE THIS!!!!!!

Postby Colette » Sun Sep 29, 2013 10:39 pm

If one assumes that the partial derivatives of a holomorphic function are continuous, the Cauchy integral theorem can be proved as a direct consequence of Green's theorem and the fact that the real and imaginary parts of Image must satisfy the Cauchy–Riemann equations in the region bounded by Image, and moreover in the open neighborhood U of this region. Cauchy provided this proof, but it was later proved by Goursat without requiring techniques from vector calculus, or the continuity of partial derivatives.

We can break the integrand Image, as well as the differential Image into their real and imaginary components:
Image
Image
In this case we have
Image
By Green's theorem, we may then replace the integrals around the closed contour Image with an area integral throughout the domain Image that is enclosed by Image as follows:
Image
Image
However, being the real and imaginary parts of a function analytic in the domain Image, Image and Image must satisfy the Cauchy–Riemann equations there:
Image
Image
We therefore find that both integrands (and hence their integrals) are zero
Image
Image
This gives the desired result
Image

THEREFORE, THIS THREAD IS DUMB.

Q.E.D.
Image
Image
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Re: U NEED TO SEE THIS!!!!!!

Postby samuelzz10 » Sun Sep 29, 2013 11:25 pm

Colette wrote:If one assumes that the partial derivatives of a holomorphic function are continuous, the Cauchy integral theorem can be proved as a direct consequence of Green's theorem and the fact that the real and imaginary parts of Image must satisfy the Cauchy–Riemann equations in the region bounded by Image, and moreover in the open neighborhood U of this region. Cauchy provided this proof, but it was later proved by Goursat without requiring techniques from vector calculus, or the continuity of partial derivatives.

We can break the integrand Image, as well as the differential Image into their real and imaginary components:
Image
Image
In this case we have
Image
By Green's theorem, we may then replace the integrals around the closed contour Image with an area integral throughout the domain Image that is enclosed by Image as follows:
Image
Image
However, being the real and imaginary parts of a function analytic in the domain Image, Image and Image must satisfy the Cauchy–Riemann equations there:
Image
Image
We therefore find that both integrands (and hence their integrals) are zero
Image
Image
This gives the desired result
Image

THEREFORE, THIS THREAD IS DUMB.

Q.E.D.

who the hell cares besides colette
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Re: U NEED TO SEE THIS!!!!!!

Postby Apollyon » Mon Sep 30, 2013 2:25 am

samuelzz10 wrote:
Colette wrote:If one assumes that the partial derivatives of a holomorphic function are continuous, the Cauchy integral theorem can be proved as a direct consequence of Green's theorem and the fact that the real and imaginary parts of Image must satisfy the Cauchy–Riemann equations in the region bounded by Image, and moreover in the open neighborhood U of this region. Cauchy provided this proof, but it was later proved by Goursat without requiring techniques from vector calculus, or the continuity of partial derivatives.

We can break the integrand Image, as well as the differential Image into their real and imaginary components:
Image
Image
In this case we have
Image
By Green's theorem, we may then replace the integrals around the closed contour Image with an area integral throughout the domain Image that is enclosed by Image as follows:
Image
Image
However, being the real and imaginary parts of a function analytic in the domain Image, Image and Image must satisfy the Cauchy–Riemann equations there:
Image
Image
We therefore find that both integrands (and hence their integrals) are zero
Image
Image
This gives the desired result
Image

THEREFORE, THIS THREAD IS DUMB.

Q.E.D.

who the hell cares besides colette


Actually i looked at it for more than five seconds. The maths are easy enough but alas i am not familiar with some of the terminology or the mentioned theorems.

Edit: actually on second thought i am more familiar with the terminology than i initially thought. It still does not make much sense mind you and... what is this useful for?
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Re: U NEED TO SEE THIS!!!!!!

Postby stubby » Mon Sep 30, 2013 9:48 am

Apollyon wrote:Actually i looked at it for more than five seconds. The maths are easy enough but alas i am not familiar with some of the terminology or the mentioned theorems.

Oh, memories. I used to tutor these equations in high school, back before I realized you got a lot more ladies as an artist than as a math prodigy.

I used to use Cauchy to school dudes who questioned the continuity of BrikWars's exploding dice progression. (For no reason, since simple algebra did it more directly.)

But Riemann is my favorite mathematician, because in 1851 he's lecturing about how these equations could be used to rotate three-dimensional space through an imaginary fourth dimension, but of course it's just a folly since rotating through the fourth dimension has no practical application.

Ten years later, up shows James Maxwell saying I don't know what the deal is, but it looks like those "bullshit extra dimensions" equations perfectly describe the relationship between electricity and magnetism... and everyone in the world's MIND is BLOWN. Out of nowhere we get the occultist paradimensional obsession of the late 19th and early 20th centuries, which hits its peak with Rasputin and Houdini, but its purest expression in Lovecraft's stories about fourth-dimensional lifeforms.

And as if that's not enough, Einstein shows up in 1906 with some new thoughts on electromagnetic propagation through curved space, the world goes crazy again... not realizing that his fancy equations are the exact same ones that Riemann presented in 1854, again having told everyone that they're mathematically fascinating but there's no possible practical use for them. Next thing you know, mushroom clouds are going up over the Japanese countryside.

The internet wants you to believe that Tesla was the father of the twentieth century. Tesla can suck it! Riemann gave us Cthulhu AND nukes.
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Re: U NEED TO SEE THIS!!!!!!

Postby Zupponn » Mon Sep 30, 2013 2:16 pm

stubby wrote:
Apollyon wrote:Actually i looked at it for more than five seconds. The maths are easy enough but alas i am not familiar with some of the terminology or the mentioned theorems.

Oh, memories. I used to tutor these equations in high school, back before I realized you got a lot more ladies as an artist than as a math prodigy.

What do you mean? Einstein got all the ladies.
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Re: U NEED TO SEE THIS!!!!!!

Postby Tzan » Mon Sep 30, 2013 2:35 pm

Einstein created a mathematical proof which indicated that he could create a gravitational milkshake that "brings all the girls to the yard".
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Re: U NEED TO SEE THIS!!!!!!

Postby Apollyon » Mon Sep 30, 2013 6:46 pm

stubby wrote:
Apollyon wrote:Actually i looked at it for more than five seconds. The maths are easy enough but alas i am not familiar with some of the terminology or the mentioned theorems.

Oh, memories. I used to tutor these equations in high school, back before I realized you got a lot more ladies as an artist than as a math prodigy.

I used to use Cauchy to school dudes who questioned the continuity of BrikWars's exploding dice progression. (For no reason, since simple algebra did it more directly.)

But Riemann is my favorite mathematician, because in 1851 he's lecturing about how these equations could be used to rotate three-dimensional space through an imaginary fourth dimension, but of course it's just a folly since rotating through the fourth dimension has no practical application.

Ten years later, up shows James Maxwell saying I don't know what the deal is, but it looks like those "bullshit extra dimensions" equations perfectly describe the relationship between electricity and magnetism... and everyone in the world's MIND is BLOWN. Out of nowhere we get the occultist paradimensional obsession of the late 19th and early 20th centuries, which hits its peak with Rasputin and Houdini, but its purest expression in Lovecraft's stories about fourth-dimensional lifeforms.

And as if that's not enough, Einstein shows up in 1906 with some new thoughts on electromagnetic propagation through curved space, the world goes crazy again... not realizing that his fancy equations are the exact same ones that Riemann presented in 1854, again having told everyone that they're mathematically fascinating but there's no possible practical use for them. Next thing you know, mushroom clouds are going up over the Japanese countryside.

The internet wants you to believe that Tesla was the father of the twentieth century. Tesla can suck it! Riemann gave us Cthulhu AND nukes.


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Re: U NEED TO SEE THIS!!!!!!

Postby stubby » Mon Sep 30, 2013 8:38 pm

Zupponn wrote:What do you mean? Einstein got all the ladies.

Einstein wasn't a math prodigy. He was a special relativity prodigy. Ladies had no defense against his special relations.

Tzan wrote:Einstein created a mathematical proof which indicated that he could create a gravitational milkshake that "brings all the girls to the yard".

It worked perfectly in theory, but due to incompatibility at the quantum level, in experiments it only ended up creating the movie "Twins."
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Re: U NEED TO SEE THIS!!!!!!

Postby The Shadowscythe » Tue Oct 01, 2013 2:50 am

stubby wrote:
Zupponn wrote:What do you mean? Einstein got all the ladies.

Einstein wasn't a math prodigy. He was a special relativity prodigy. Ladies had no defense against his special relations.


:ftw:

Apollyon wrote:Is there anything you are not awesome at?


Origami.

I don't think he can do Origami.

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Re: U NEED TO SEE THIS!!!!!!

Postby samuelzz10 » Tue Oct 01, 2013 4:23 pm

Stubby, you know a lot about chicks. How can I start dating one, and have sex later?
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Re: U NEED TO SEE THIS!!!!!!

Postby stubby » Tue Oct 01, 2013 7:24 pm

samuelzz10 wrote:Stubby, you know a lot about chicks. How can I start dating one, and have sex later?

Did you read the part about turning the human understanding of physics on its head with the discovery of matter-energy equivalence, and torching millions of unsuspecting civilians in a nuclear holocaust as a result? That's probably a good first step. What you're aiming for is a last man on earth scenario.

Alternately, save up a couple of bucks, because it's a buyer's market: http://www.economist.com/news/britain/21578434-old-industry-deep-recession-sex-doesnt-sell
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