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This topic has moved here: Subject: A rather striking and errant mathematical fact
  • Subject: A rather striking and errant mathematical fact
Subject: A rather striking and errant mathematical fact

The concept is all that really matters.


Posted by: A Citizen
>Is bad at math
>Opens thread anyways
>Leaves depressed
I laughed aloud, but really I can't agree more.

  • 02.13.2012 10:59 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

Posted by: Luke35120
Why didn't you use a the equation writer that is build into win 7 to make it simpler?
Lulz. LaTeX isn't built into Windows 7, silly. Anyway, it's no fun to just link to a pdf or graphic; nobody would read it.

  • 02.14.2012 10:08 AM PDT

I don't even.

  • 02.14.2012 10:14 AM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

Posted by: Luke35120
Typed proofs are so hard to follow.


Why didn't you use a the equation writer that is build into win 7 to make it simpler? Unless you are one of those guys who is smart and uses Ubuntu/Debian/etc ;)


I actually did that, because I'm still enthralled with this proof, and sent it to one of my Mathematics major friends.

The word document can be downloaded here

Also on there are some notes and an alternative proof on the subject that takes the polar integration a slightly different direction, and ends up with a different result.

Edit: I just noticed a typo. On page two, I said "hemisphere" when I meant "semicircle"

[Edited on 02.14.2012 4:34 PM PST]

  • 02.14.2012 4:27 PM PDT

Turkey

Your coup scared me. I didn't see it but then I saw it when I was reading. T.T

  • 02.14.2012 4:35 PM PDT

Posted by: Dodge Reborn
The flood is always butthurt about something.


KotOR

Integrals I can handle. But negative infinity to infinity integrals? Too much.

Still, pretty awesome.

[Edited on 02.14.2012 5:15 PM PST]

  • 02.14.2012 5:10 PM PDT

Congratulations. You're literate!

Oh wow, that's pretty neat.

  • 02.14.2012 5:13 PM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

Posted by: Alt account1
I read the OP, I don't understand.

Someone explain the fact in short? I don't need to know why, just tell me the damn fact.


Basically, what is happening is that a surface is being made. The surface is a square with infinitely long sides (think of it more philosophically than literally). The height of the surface above the ground of zero at any point (x,y) is determined by e^-(x^2 + y^2). Here's a small portion of this surface.

What integrals do is they find the area below a curve, from point a to b. In this instance, the bounds are from negative infinity to infinity, which means you are finding the area beneath the entirety of the curve. By having a double integral (that's what dx and dy imply), you are finding the volume under the infinitely large square, or the entirety of the volume.

X and Y (and Z) coordinates (what is referred to as the "Cartesian coordinate system" isn't the only way to represent space. It could also be done in polar coordinates, where a position is identified by a radius (usually from the 0,0 origin) and angle (from the x axis counter-clockwise). The same space of an infinitely wide and tall square to a circle of infinite radius (again, "philosophically" the same thing) spun about the 0,0 point a full 360 degrees (though we use radians. It's simpler mathematically. 360 degrees = 2pi radians)

When you switch coordinates, the variables need to be adjusted. See in the OP where e^1(x^2+y^2) switches to e^-r^2? Think of the Pythagorean Theorem. x^2 + y^2 = z^2. z is the equivalent of a radius (Are you familiar with the Unit Circle), so this Theorem is tasked in this scenario as x^2 + y^2 = r^2, which you see in the OP.

Solving integrals is a bit complicated for those unfamiliar with it. Once a certain amount of familiarity is acquired with them, it's mostly pattern recognition. At this point you're just going to have to trust me/us on the issue.

So the solution here solves out to be pi. It is then assumed that since the two integrals at the beginning are so similar, you could treat them as if they are equivalent to one of them squared. This means that The square root of one of them squared, lim(a->oo)int(-a,a)e^(-x^2)dx, is equal to the square root of the answer, equating to sqrt(pi).

I have some issues with this proof, even though it mathematically is sound. They can be seen in the document linked in this post.

  • 02.14.2012 6:36 PM PDT
  •  | 
  • Honorable Heroic Member
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"Hoc volo sic iubeo. Sit pro rationes voluntas." - Juvenal

"Scio me nihil scire." - Socrates

I'll be honest. I haven't taken that level of math yet. I have no clue what you just said.

  • 02.14.2012 6:41 PM PDT

Tyler Kelly


Posted by: Chalupa King117
Dude, Disam..... I'm sorry, but you and I both know this is something the Flood can't even begin to comprehend.

  • 02.14.2012 6:42 PM PDT

-blam!- Was that actually blammed out? Or did I just type it? You'll never know.

I read it.

I read the whole thing.

I can honestly say, I have never thought of that before.

  • 02.14.2012 6:43 PM PDT

Posted by: AngryBrute1
Oh yeah, since somebody does not believe what YOU believe; that makes us vapid...
I cannot grasp that what you call "Something happened to nothing, and that nothing became something, and it was smaller than than a period."

Posted by: Disambiguation
the simple function exp(-x^2)


Posted by: Disambiguation
simple

Posted by: Disambiguation
(-x^2)

YOU LIE!
My brain hurts just looking at it.

  • 02.14.2012 6:43 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

Posted by: prometheus25
I have some issues with this proof, even though it mathematically is sound. They can be seen in the document linked in this post.
I don't see the problem.

  • 02.14.2012 6:44 PM PDT

END OF LINE


Posted by: Captain K

Posted by: A Citizen
>Is bad at math
>Opens thread anyways
>Leaves depressed
I laughed aloud, but really I can't agree more.

  • 02.14.2012 6:50 PM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

Posted by: Disambiguation
Posted by: prometheus25
I have some issues with this proof, even though it mathematically is sound. They can be seen in the document linked in this post.
I don't see the problem.


Read over the document I linked. Orthogonality of x and y is an issue to me. Also, the polar integration can be done equivalently by int(-a,a)int(0,pi)e^(-x^2)rdthetadr, which gives you an answer of 0.

  • 02.14.2012 6:54 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

Posted by: prometheus25
Read over the document I linked. Orthogonality of x and y is an issue to me. Also, the polar integration can be done equivalently by int(-a,a)int(0,pi)e^(-x^2)rdthetadr, which gives you an answer of 0.
Orthogonality of x and y has nothing to do with the polar transformation; and you're still erroneously integrating r from -inf to inf, which doesn't even make sense. r is a nonnegative quantity. By symmetry, your integral should be equivalent to this one, which it isn't.

[Edited on 02.14.2012 6:59 PM PST]

  • 02.14.2012 6:55 PM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

Posted by: Disambiguation
Posted by: prometheus25
Read over the document I linked. Orthogonality of x and y is an issue to me. Also, the polar integration can be done equivalently by int(-a,a)int(0,pi)e^(-x^2)rdthetadr, which gives you an answer of 0.
Orthogonality of x and y has nothing to do with the polar transformation; and you're still erroneously integrating r from -inf to inf, which doesn't even make sense. r is a nonnegative quantity.


You can absolutely have a negative radius. It's not mathematically incorrect. In that case, I am integrating a positive infinite radius in one direction by 180 degrees (pi radians) while simultaneousness integrating a negative radius in the exact opposite direction 180 degrees (pi radians). It's the equivalent of a two-bladed propeller (with blades of infinite length, of course) spinning 180 degrees, but each one, being mounted exactly opposite each other, cover half the area of a full circle. Mathematically this is equal to a single "blade" being spun a full 360 degrees.

Edit: Further more, orthogonality has everything to do with polar integration. The reason that you can substitute x^2 + y^2 for r^2 is because they are right angles to each other, allowing for the Pythagorean Theorem to be employed to find the length of the hypotenuse, which is the radius. It also means that they are out of phase.

I assure you this is mathematically correct. I am a 4th year Electrical Engineer, too, ya know. That puts my credentials exactly where you are.

[Edited on 02.14.2012 7:05 PM PST]

  • 02.14.2012 7:00 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

Posted by: prometheus25
I assure you this is mathematically correct. I am a 4th year Electrical Engineer, too, ya know. That puts my credentials exactly where you are.
I am a 4th year BSEE and I have a BA in mathematics.

Your credentials are not the same as mine, and none of this is at all relevant to the question at hand.

Also, see my edit.

[Edited on 02.14.2012 7:03 PM PST]

  • 02.14.2012 7:02 PM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

Posted by: Disambiguation
Posted by: prometheus25
I assure you this is mathematically correct. I am a 4th year Electrical Engineer, too, ya know. That puts my credentials exactly where you are.
I am a 4th year BSEE and I have a BA in mathematics.

Your credentials are not the same as mine, and none of this is at all relevant to the question at hand.

Also, see my edit.

I was merely implying that I am not pulling these figures out of my ass

  • 02.14.2012 7:03 PM PDT

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself."
-Nietzsche

Posted by: prometheus25
I was merely implying that I am not pulling these figures out of my ass
And I respect you for it, but you're still wrong.

  • 02.14.2012 7:05 PM PDT
  •  | 
  • Fabled Legendary Member

They call me graland.

All I gathered from the OP is that mathematics can suck my dick.

  • 02.14.2012 7:07 PM PDT

I was at a baseball game wondering why the ball gets bigger as it comes closer.......then it hit me.......
Objection!
Lmgtfy
lmsbtfy

mfw

  • 02.14.2012 7:10 PM PDT

Old school Bungie, born and raised,
In the Septagon is where I spend most of my days.
Relaxin', maxin', posting all cool,
Talking about Halo, life and some school.
Got in one little argument, and the mods got scared,
they said "You're gonna get banned and your member title'll be bare!"

I am rather enjoying this. It's been a while since I've been pulled from signal processing and transforms into pure math.

And I would like to know the last time a thread on integration made it to 100 posts.

[Edited on 02.14.2012 7:19 PM PST]

  • 02.14.2012 7:18 PM PDT