e^(pi i) + 1 = 0

[jj]

It's not just an equation :)

Just trying to oil the ways, that's all. :D

[zer0vector]

It's the most beautiful equation in all of math. Whoever would have thought there would be a relationship between 2 irrational numbers, 2 integers, and the imaginary i?

Also, assuming I read you correctly, nice pun.

[T'ai Chi]

Originally posted by jj
It's not just an equation :)

Just trying to oil the ways, that's all. :D

Thanks jj, one of my favorite equations. :)

There is a good, no, a GREAT! book by William Dunham titled "Euler: The Master of Us All".

Here is an informative link on e stuff: http://mathworld.wolfram.com/e.html

[jj]

Well, after that "phi" thing ....

I had to say something digestible :)

[Suggestologist]

Originally posted by jj
It's not just an equation :)

Just trying to oil the ways, that's all. :D

Where Mathematics Comes From by George Lackoff and Nunez provides an interesting explanation for that equation at the end of the book.

[Dilettante]

I think the more interesting equation is

e^ix = cos x + i sin x

for which jj's equation is a special case (x = pi).

If you multiply it out for two values, x and y, it preserves the rule

e^i(x+y) = (e^ix) * (e^iy).

[ceptimus]

e^{i π} + 1 = 0

Now that is pretty.

And here's how I did it: [size=4][b]e^{i π} + 1 = 0[/b][/size]

Now I could show you how I showed you how I did it, but Hal doesn't like repeated cursing.

[hammegk]

Hmmm, would it be true if nothing (say, for example the "known universe") existed?

Is that equation always a Law of Math, & by extension, Physics in every conceivable universe?

[ceptimus]

That would be true for me hammegk. I guess that labels me as a Platonist?

[hammegk]

Originally posted by ceptimus
That would be true for me hammegk. I guess that labels me as a Platonist?

Perhaps. My take on him though was that he was an (illogical) Dualist. :p

[T'ai Chi]

Could someone explain to me the importance of complex numbers in studying electricial matters?

[ceptimus]

Originally posted by T'ai Chi
Could someone explain to me the importance of complex numbers in studying electricial matters? If you apply an AC waveform to a resistor, the current rises and falls in line with the voltage.

Apply the same AC to an inductor, and the current lags behind the voltage - if you plot a graph showing voltage and current against time, the current lags by 90 degrees.

A capacitive load works the other way - the current waveform leads the voltage.

The currents and voltages can be conveniently modeled by vectors on the Argand diagram, and that's where complex numbers live.

Most real networks contain a mixture of capacitive, inductive and resistive loads. The use of complex numbers makes the analysis of such circuits very much simpler. jj is the man here to speak about filter design.

[T'ai Chi]

Thanks cept!

[Dilettante]

Originally posted by hammegk
Hmmm, would it be true if nothing (say, for example the "known universe") existed?

Is that equation always a Law of Math, & by extension, Physics in every conceivable universe?

In every conceivable universe, it is a theorem about complex numbers.
In a universe with very different laws of physics, complex numbers might not be as interesting as they are to us, and this theorem might go undiscovered or remain obscure.

[teddosan]

Basically, the reason we use complex numbers to model electrical systems is that the notation becomes a lot less complex (no pun intended) when we do... For the most simple example, think of a cosine problem... cos(x) = y
Well, if we just add j*sin(x) to the left and j*0 to the right, we get: cos(x) + j sin(x) = y + j0 or e^(jx) = y Now, after we're done solving the problem, we just remove the imaginary part (anything multiplied by j) and we get the actual answer...
The cool thing with electrical (AC) problems is that the imaginary part will actually tell you something about timing of the sine or cosine waves...
Damn, I'm a dork...

[T'ai Chi]

Thanks teddosan!


The cool thing with electrical (AC) problems is that the imaginary part will actually tell you something about timing of the sine or cosine waves...
Damn, I'm a dork...

:)