New math fact: e^((pi)i)=-1

astrosgp · #1 03-10-2002, 11:18 PM

With all the talk that 1=.9999... got, I find this equation MUCH more intriguing.

My math teacher (who graduated from the University of Moscow in Physics) proved this to us, but I cannot explain it. But I KNOW it is true:

[B]e^((pi)i)=-1[/B], where e~2.718281828... pi~3.141592653589...and i=sqrt(-1).

Anyone know how to prove??? (PhD in math may be necessary :))

RickyD · #2 03-11-2002, 11:22 AM

I can't say that I exactly follow all of this (has to do with Taylor Series and the identity of e), but here's a link to a proof of that equation from faqs.org:

[url]http://www.faqs.org/faqs/sci-math-faq/specialnumbers/eulerFormula/[/url]

or a slightly less confusing version (set to the tune of American Pie :) )

[url]http://www.people.cornell.edu/pages/wcc3/euler.html[/url]

Skye · #3 03-11-2002, 01:02 PM

I know how to do this except for the i=sqrt part. couldn't you just do it on a calculator? Anyway, whys that a big deal if it equals 1?

E and pi go on forever so you have to do it on calculator really to keep it accurate.

Pantera Psycho · #4 03-11-2002, 06:03 PM

I just did it on my calculator, yes, it's -1, I couldn't tell anyone how to prove it, proofs were always my weakest point in mathematics.

***Chip*** · #5 03-11-2002, 06:23 PM

Man! We really need the coaster season to hurry up and start! People are posting threads about [I]math[/I]!! Come on! We need better topics around here if you people are starting to post about stuff that makes my brain explode. Stupid math. Why are you posting all these weird threads about math?

***Chip*** · #6 03-11-2002, 06:34 PM

What is it with the math threads? Why are you people trying to prove these weird equations and stuff? These really prove that this is the off-season. You're posting about [I]math[/I]!! Why? Man, we need coasters to hurry up and open or I'm gonna go insane. These threads are the type that make my head explode! Why would people want to know this stuff? Yarg! My brain!

(Mods, this is acting weird. I posted once, it didn't show up, so I assumed there was an error and posted again. Then both posts showed up, so I deleted one, and both got deleted. You play with it, as I don't see what's happening)

CrystalKat · #7 03-11-2002, 07:35 PM

Okay, this is from my husband -- AP Calculus-based Physics teacher -- who for his college degree went through Differential Equations (one step above Calculus III):

*****
This is called "Euler's Theorem" and is an interesting (true) formula because it is the only formula that can be written using the "fundamental symbols" of mathematics: 0, 1, plus, multiply, equals, e and pi. The more common form of the equation is e^[(i)(pi)]+1=0.

The general form of the equation says e^[i(x)]=cos x +isin x. Substitute pi in for x. The sine term goes to zero (as does the complex term) and the cosine term equals -1. Since -1+1=0, the theory works. As for why e^[i(x)]=cos x +isin x, well, that is a job for the Argand plane (a complex Cartesian plane) and vector components.
*****

Don't ask me anything about it, I wouldn't have a clue... :D In short, however, yes it is true, it does work, and let's leave the mysteries of mathematics for physicists, mathematicians, and roller coaster engineers to figure out.

coastergenius100 · #8 03-11-2002, 07:43 PM

[QUOTE][i]Originally posted by Skye [/i]
[B]I know how to do this except for the i=sqrt part. couldn't you just do it on a calculator? Anyway, whys that a big deal if it equals 1?

E and pi go on forever so you have to do it on calculator really to keep it accurate. [/B][/QUOTE]

The signifigance is that unit "i" is equal to the square root of -1. It is reffered to as an imaginary number, for it cannot be attained by using regular numbers.