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Old 11-16-2008, 09:23 AM #1
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Default Eulers Formula

I'm a math major and this blows my mind every time I think about it. It links five of the most fundemantal constants together. Rational integers, fundamental transcendental constants, and the imaginary constant all in one formula.

Amazing!!! :P

I'm a nerd
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Old 11-16-2008, 09:43 AM #2
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Default Re: Eulers Formula

Quote:
Originally Posted by Xplorer877
I'm a math major and this blows my mind every time I think about it. It links five of the most fundemantal constants together. Rational integers, fundamental transcendental constants, and the imaginary constant all in one formula.

Amazing!!! :P

I'm a nerd

That confuses one of my friends too, he's doing advanced higher maths I'll be doing that stuff in 2 years hopefully !

-Adam
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Old 11-16-2008, 10:34 AM #3
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Default Re: Eulers Formula

So I'm just gonna say what everybody probably thinks when he sees that: e[sup]i[ch960][/sup]=-1 ;D
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Old 11-18-2008, 11:06 AM #4
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Default Re: Eulers Formula

Holy shat.
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Old 11-19-2008, 02:25 AM #5
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Default Re: Eulers Formula

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Originally Posted by VillageIdiot
Holy shat.
when you see longcat, brix will be shat.

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Old 11-19-2008, 02:35 AM #6
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Default Re: Eulers Formula

So this is so cool because e to the i*pi power=-1, with pi and e (don't know what &quot;i&quot; is &gt;.&lt being infinite, non repeating decimals, right? Sorry if this is really ignorent, I don't know too much about math. (7th grade education sucks &gt;.&lt; even if you're in the advanced classes and other stuff.)
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Old 11-19-2008, 04:54 AM #7
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Default Re: Eulers Formula

I showed this to my dad. He did Extension 4 Maths in high school, and was an engineer for ten years. His response was 'wtf omg'
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Old 11-19-2008, 04:56 AM #8
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Default Re: Eulers Formula

i represents imaginary numbers. Take sqrt (-1).
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Old 11-19-2008, 07:14 AM #9
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Default Re: Eulers Formula

^Except for some people, like electrical engineers, the imaginary number -1^(1/2) is j. *I mean, I understand why they do that wiht electrical current being represented by i already, but still, WHY DO THEY DO THAT?!?? Ugh.

--------------------------------------------------

You get into some crazy variable assignments when you get into advanced topics. *The more advanced you get, the more letters you need, and there just aren't enough. *With the classes I have now, we literally have used most of all of the following letters: lower case english, script lower case english, upper case english, script uppercase english, lowercase greek, and uppercase greek. *You know how hard it is to tell the difference between a lowercase greek &quot;eta&quot; and a lowercase script english letter &quot;n&quot; in my handwriting? *And keeping a single formula going in a derivation which includes multiple cases of each of uppercase greek sigma, uppercase english E, and uppercase script english E. *Not to mention variables can all have subscripts, superscripts, bars on top, tildas on top (this---&gt; ~), or multiple of those. *Just reading notes makes my head hurt these days.

I've had a class previously where one of our main formulas we had to remember how to use and expand multiple ways was literally x[sup]x[/sup] = X. *All of them being the letter x: one lowercase, one lowercase script, and one uppercase, and all meaning VERY different things.
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Old 11-19-2008, 09:41 AM #10
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Default Re: Eulers Formula

If you have taken Calc 2 you should be able to fallow the Taylor Series proof.

http://en.wikipedia.org/wiki/Euler%27s_formula

Also see

http://www.youtube.com/watch?v=zELiwFCQa1Y

I'm a engineering major = LOTS OF MATH!!


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What would you rather do, a 4 page essay or 50 math problems?
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Old 11-19-2008, 12:52 PM #11
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Default Re: Eulers Formula

OMG we just got to Taylor's formula.And Taylor and MacLaurin's series for functions with up to 2 variables. I think Euler's formula will be mentioned. ;D
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Old 11-19-2008, 02:34 PM #12
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Default Re: Eulers Formula

Quote:
Originally Posted by Xplorer877
I'm a math major and this blows my mind every time I think about it. It links five of the most fundemantal constants together. Rational integers, fundamental transcendental constants, and the imaginary constant all in one formula.

Amazing!!! :P

I'm a nerd
Euler's formula == mathematical awesomeness

I remember this from Calc 2 a looong time ago.
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Old 11-19-2008, 03:11 PM #13
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Default Re: Eulers Formula

I've always been a fan of e. Take the derivative of e and what do you get? e The proof is elegant. e is one of those absolutely fundamental numbers that finds it's way into everything. The world would be a different place without it.
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Old 11-19-2008, 04:03 PM #14
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Default Re: Eulers Formula

A trick I've had to use a few times in college involves the derivative of e and the geometric series. *After studying the geometric series we know it's sum. *You can find a sum of a geometric series with R^n=e^-(a*n*x). *You can also find the sum of the series n*e^(-a*n*x).
This only works with geometric series of e.
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Old 11-22-2008, 04:59 PM #15
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Default Re: Eulers Formula

Quote:
Originally Posted by pullbangdead
^Except for some people, like electrical engineers, the imaginary number -1^(1/2) is j. *I mean, I understand why they do that wiht electrical current being represented by i already, but still, WHY DO THEY DO THAT?!?? *Ugh.

--------------------------------------------------

You get into some crazy variable assignments when you get into advanced topics. *The more advanced you get, the more letters you need, and there just aren't enough. *With the classes I have now, we literally have used most of all of the following letters: lower case english, script lower case english, upper case english, script uppercase english, lowercase greek, and uppercase greek. *You know how hard it is to tell the difference between a lowercase greek &quot;eta&quot; and a lowercase script english letter &quot;n&quot; in my handwriting? *And keeping a single formula going in a derivation which includes multiple cases of each of uppercase greek sigma, uppercase english E, and uppercase script english E. *Not to mention variables can all have subscripts, superscripts, bars on top, tildas on top (this---&gt; ~), or multiple of those. *Just reading notes makes my head hurt these days.

I've had a class previously where one of our main formulas we had to remember how to use and expand multiple ways was literally x[sup]x[/sup] = X. *All of them being the letter x: one lowercase, one lowercase script, and one uppercase, and all meaning VERY different things.
Dude, -1^1/2 is the same as sqrt (-1)

the thing is that when working with electronics you call it 'j' because you call 'i' the current intensity and it could create confusion.



i've never seen that formula, not even in college....i went past thru taylor, maclaurin, series, etc... but never seen euler =(
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Old 11-23-2008, 09:49 PM #16
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Default Re: Eulers Formula

That's a pretty cool formula. We're nowhere near that yet. (Then again, I am only in Precalculus...)

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