e^(i*pi)+1=0

[UndertheOcean]

Such a beautiful equation .... and very easy to prove on top of that.

Just take the Taylor series expansion around zero of e^z , and substitute z=i*x , If you lump the real parts of the series together you find out that they represent the series equivalent to cos(x), in a similar fashion the imaginary parts represent sin(x)

so e^(i*x)=Cos(x)+ i Sin(x)

for x = pi ==> Cos(pi)=-1 and Sin(pi)=0

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

So

e^(i*pi)+1=0 <==QED.

like I said , very simple and not advanced , yet extremely elegant and beautiful.



:)

[kayakjohnny]

1. I was just going to post this.

Wow, what are the chances?

:wow:

[rug]

3. Use the formula to figure it out.

[Skip Intro]

2. 42. nt

[kayakjohnny]

4. Ha!

Just for that, you're getting a Pan Galactic Gargle Blaster.

:beer:

Enjoy!

[Skip Intro]

5. Well, thanks! I'll drink to that...

:toast:

[kayakjohnny]

6. Got towels?

:toast:

[Skittles]

7. I'll be in Orlando soon

I WILL KICK YOUR ASS

[pokerfan]

8. and useful

[begin_within]

9. It is my favorite equation.

I have no use for it, but I think it's elegant and beautiful. I remember the first time I saw it, in high school I think, I just stared at it for a while. All of the fundamental building blocks of mathematics are right there, and they all fit together beautifully, as if the entire mathematical universe was condensed into one simple elegant statement.

[PVnRT]

10. Those are the only five numbers you need

[Orsino]

11. That's what *she* said! n/t

[Duer 157099]

12. As a non-mathematician, all I can see is

"it all comes to zero"

Thanks, man. I wasn't depressed enough, now there's mathematical proof of how meaningless it all is?

[Swede]

13. Aught times aught equals aught

[pokerfan]

14. a picture of what's going on

e^iπ means go counter-clockwise 180 degrees.
+1 advances you to zero.

[Duer 157099]

15. Exactly.

First it looks like you are getting somewhere, then you start going backwards, then it appears that all you're doing is going in circles, and then it all abruptly ends at zero.

Just as I suspected.

[pokerfan]

16. I felt the same way when I took AC Circuits

[MiddleFingerMom]

17. This sucks. Nobody told me there'd be math.

.
Math is HARD.
.

.

[hunter]

18. The universe does what it does without math.

No worries.

[pokerfan]

19. and a book recommendation

Dr. Euler's Fabulous Formula by Paul J. Nahin

This is a wonderful book - a sequel to Nahin's earlier An Imaginary Tale: the Story of √-1. This one is more advanced. And the author clearly sets up requirements: "... two years of calculus, a first course in differential equations, and perhaps some preliminary acquaintance with matrix algebra and elementary probability. Third year math majors would certainly have the required background." I would low the bar if a little. An intelligent second year student will enjoy the book, even if it takes a little more effort. Doubt not: the extra effort will pay off.

http://www.cut-the-knot.org/books/Reviews/FabulousFormula.shtml