Slightly crazy mathmatical stuff

[Hyper-space]

fucking magnets!

how do they work?

 

[deleted_scifidownbeat]

DELETED

 

[not_the_dm]

fucking magnets!

how do they work?

via the exchange of virtual photons.

BTW, the mathematical definition of the constant e is the sum of the infinite series of numbers defined by 1/x!

(! in this instance is called "factorial," which means you multiply the number by all the numbers before it, starting with 1)

e = 2.7182818284....
1/0! = 1
1/0! + 1/1! = 1 + 1 = 2
1/0! + 1/1! + 1/2! = 1 + 1 + 1/2 = 2.5
1/0! + 1/1! + 1/2! + 1/3! = 1 + 1 + 1/2 + 1/6 = 2.6666666666....
1/0! + 1/1! + 1/2! + 1/3! + 1/4! = 1 + 1 + 1/2 + 1/6 + 1/24 = 2.7083333333....

If we keep adding all the values of 1/x!, we will eventually reach the value of e.

I honestly had no idea that that was the case...
Thats kinda cool.

So this nth dimension stuff is just for people who don't understand math and think it's something mystical.

Except that string theory, in particular 11-dimension M-theory, actually does require/predict that those extra dimensions are an integral part of spacetime and are, in fact, spatial. So in not all cases is it simply a representation of another free variable; sometimes this whole nth dimensions stuff actually is kinda "mystical"

That reminds me of someting. The polyakov equations predict 26 dimentions of space time for bosonic string theory. 25 of space and the 26th being time. Ofcause bosonic string theory is incorect as it only predicts only bosons and ignores fermions copletely.

 

[Borntolose]

And Finally 1=2
a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

You divided by zero. Your point is moot.

Damn... Ninja'd
But yeah.
If a=b then a-b=0.

 

[dillinger88]

e^i-pi = -1

Or so xkcd tells me. I'm terrible at math.

It does. If you're a maths geek then the explanation is some serious crazy (but cool) shit.

Sorry to be the bearer of bad news, but it's actually e^(i*pi) = -1:

Euler's equation : e^(i*x) = cos(x)+i*sin(x)

e^(i*pi) = cos(pi)+i*sin(pi)

cos(pi) = -1

sin(pi) = 0

e^(i*pi) = -1+i*0 = -1


Hope that helps.


EDIT: It's basically to do with the fact a sinusoidal wave can be defined as a unit circle on a plane with x axis being real values and the y as the imaginary values, or some shit.

 

[not_the_dm]

hussar for the proof of e^(i*pi)=-1 only working in radians.
more nutter stuff.

-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)

(du/dx) denotes the partial derivative of u with respect to x, (du^2/dt^2) denotes the second partial derivative of u with respect to t, etc.
anyways, this is a model equation from finite element analysis
When b=0, c2=0, co=0, c1=rho*A, a=kA
this equation represents unsteady heat transfer in a fin

When a=0, b=E*I, co=k, c1=0, c2=rho*A
this equation represents transverse vibrations in a beam

When a=E*A, b=0, c1=0, c2=rho*A, co=0
it represents longitudinal motion(vibration or wave propogation) of a slender rod

all of these require initial conditions and boundary conditions to be specified, but I can't find all of it at the moment. I'll keep looking though.

 

[dillinger88]

hussar for the proof of e^(i*pi)=-1 only working in radians.
more nutter stuff.

-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)

(du/dx) denotes the partial derivative of u with respect to x, (du^2/dt^2) denotes the second partial derivative of u with respect to t, etc.
anyways, this is a model equation from finite element analysis
When b=0, c2=0, co=0, c1=rho*A, a=kA
this equation represents unsteady heat transfer in a fin

When a=0, b=E*I, co=k, c1=0, c2=rho*A
this equation represents transverse vibrations in a beam

When a=E*A, b=0, c1=0, c2=rho*A, co=0
it represents longitudinal motion(vibration or wave propogation) of a slender rod

all of these require initial conditions and boundary conditions to be specified, but I can't find all of it at the moment. I'll keep looking though.

At the risk of me being totally off-topic, I'm currently working on a program that does FEA with quadratic tets to model deformation. Are you a FE guru? As I've sort of hit a brick wall and may need to enlist some help...

 

[hamster mk 4]

Now as by definition a point in space has to take up some room

Actualy according to the mathimatical definition of a point:

http://en.wikipedia.org/wiki/Point_(geometry)

It takes up no volume/area/room. You have to represent a point on a graph by giving the dot some space, or else you can't see it. But as a mathimatical concept a point occupies no space.

 

[not_the_dm]

hussar for the proof of e^(i*pi)=-1 only working in radians.
more nutter stuff.

-d(a(du/dx))/dx+(d^2(b*(du^2/dx^2)/dx^2))+co*u+c1*(du/dt)+c2*(du^2/dt^2)=f(x,t)

(du/dx) denotes the partial derivative of u with respect to x, (du^2/dt^2) denotes the second partial derivative of u with respect to t, etc.
anyways, this is a model equation from finite element analysis
When b=0, c2=0, co=0, c1=rho*A, a=kA
this equation represents unsteady heat transfer in a fin

When a=0, b=E*I, co=k, c1=0, c2=rho*A
this equation represents transverse vibrations in a beam

When a=E*A, b=0, c1=0, c2=rho*A, co=0
it represents longitudinal motion(vibration or wave propogation) of a slender rod

all of these require initial conditions and boundary conditions to be specified, but I can't find all of it at the moment. I'll keep looking though.

At the risk of me being totally off-topic, I'm currently working on a program that does FEA with quadratic tets to model deformation. Are you a FE guru? As I've sort of hit a brick wall and may need to enlist some help...

Unfortunatly not... It's just saomething that I've picked up on at somepoint and scribbled down. Sorry mate.

 

[VincentX3]

this assumes that circles can even exist. Which they can't. And here's why;

O RLY?

Spoiler

There's my proof that it can!

 

[Hyper-space]

fucking magnets!

how do they work?

via the exchange of virtual photons.

sounds more like black magic to me.

 

[linkmastr001]

Apparently 0! is 1, which doesn't make sense becuase the only proof of this uses n!=n * (n-1)!, so looking at 1!, we have...

1! = 1 * 0!

and because of that they claimed 0! = 1, but using the same logic on 0!...

0! = 0* -1!

THEREFORE, I REFUSE TO BELIEVE IT!!! I PROVED 0! = 0, SUCK IT MATH PEOPLES!!!

0! is defined to be 1.

In the same vein, I could present you with a piecewise function, such as {f(x)=x, x=/5; f(x)=1, x=5} (which translates as "The function of x is equal to x if x does not equal 5; the function of x is equal to 1 if x does equal 5.") In other words, I have a line going up at a 45 degree angle. It isn't continuous, however, because there is a hole in the line at x=5. Normally, with the equation f(x)=5, f(x) would be 5 if x was 5. Because I have specifically defined x=5 to have the function value f(x)=1, I do not have a perfect line but a removably discontinuous function (i.e. a broken line).

In other words, mathematicians just arbitrarily assigned 1 as the function value of f(x)=x! when x=0.

Still seems silly to me, then I saw you post here:

BTW, the mathematical definition of the constant e is the sum of the infinite series of numbers defined by 1/x!

(! in this instance is called "factorial," which means you multiply the number by all the numbers before it, starting with 1)

e = 2.7182818284....
1/0! = 1
1/0! + 1/1! = 1 + 1 = 2
1/0! + 1/1! + 1/2! = 1 + 1 + 1/2 = 2.5
1/0! + 1/1! + 1/2! + 1/3! = 1 + 1 + 1/2 + 1/6 = 2.6666666666....
1/0! + 1/1! + 1/2! + 1/3! + 1/4! = 1 + 1 + 1/2 + 1/6 + 1/24 = 2.7083333333....

If we keep adding all the values of 1/x!, we will eventually reach the value of e.

and I realized that not assigning 0!=1 would totally mess up e, and SO MUCH other stuff it's based off of.

Mathmatitions, you win this round...

 

[SnipErlite]

Sorry to be the bearer of bad news, but it's actually e^(i*pi) = -1:

Euler's equation : e^(i*x) = cos(x)+i*sin(x)

e^(i*pi) = cos(pi)+i*sin(pi)

cos(pi) = -1

sin(pi) = 0

e^(i*pi) = -1+i*0 = -1


Hope that helps.


EDIT: It's basically to do with the fact a sinusoidal wave can be defined as a unit circle on a plane with x axis being real values and the y as the imaginary values, or some shit.

Yeah I thought the other one looked off but, meh, I was tired. It's an interesting equation though, the first time I read through the proof a few months ago it seemed kinda crazy.

Thanks though.