Survey posted 2005-05-16 19:04 by Jon.

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Anyone who says "e^(pi*i) + 1 = 0!" (factorial) is forgetting that 0! and 1! are both 1. :-)

I just don't see why anything that is to the power of 'i' could be a 'real' answer. Yes I know that e is this really awesome, all solving number...but still... I just don't get it. Oh and by the way the formula for 'e' is: 'The summation of "1/n!" where the start is 0 and the limit is infinity'

The reason is that you take the i*sin(0) to find the answer. Sin(0)=0 and 0i=0 so only real solutions result. You can find a more detailed version if you google it.

You actually take sin(pi), which is also zero though.
e^(i*pi)=cos(pi)+i sin(pi)=-1

Youre right, I made a typeo. I ment to say sin(pi)=0.

typeo :P

tipo.

typo

Good gracious...

My goodness...

jeez. All of this from having a typo when spelling typo.

Technically, it originated from someone commenting that 0! = 1! = 1. :-)

you lost me.
i'll get back to my program

What are you programming?

You can prograhm?

Mispeling tipo:
1:tiepo
2:typho
3:tiphoe
4:tripo
5:TI-P0
6:typoe
7:TI-po
8:tgipo
9:typlow
C:typo
BTW:C=Correct

More generally, e^x = Σ(x^n/n!,n,0,∞) = 1+x+x²/2+x³/6+...

By extending the Taylor series domain to the complex plane, we get:

e^(iy) = 1 + (iy) + (iy)^2/2! + (iy)^3/3! + (iy)^4/4! + (iy)^5/5! + ...
= 1 + iy - y^2/2! - iy^3/3! + y^4/4! + iy^5/5!+...
= (1 - y^2/2! + y^4/4! - y^6/6! + ...) + i * (y - y^3/3! + y^5/5! - y^7/7! + ...)
= cos(y) + i * sin(y)

thus arriving at Euler's formula.

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

You lost me at the "..."(lol)

DUH!!!!!

The easiest survey ever...I just entered it into my calc and looked at the result. :-p

Anyone with half a brain knows that that answer is one of the survay choices.

did you know that this equation was invented by that guy that lived in that country and lived around the year well you know what i mean.

Congratuldations...you just described 4 billion people.

actually more like 10 billion plus. The world pop is just over 6 billion, take in account deaths and births, now my brain hurts.

The world population is about 6 milliard, not 6 billion. "Billion" is an ambiguous term, as it usually means a million million (10^12) and not a thousand million.

Maybe in your country a billion sometimes means a million million, but in the US a billion almost always means a thousand million. See the link for an interesting Wikipedia article about the ambiguity of the terms billion and milliard. The discussion is quite interesting

I knew that. :-)
Regardless of country, "billion" is still a dodgy term to use.

Let's just say 10^10 or 2^33. :)

10^9

I meant the 10 billion/10 milliard number, not just billion/milliard.

Or 2^30 (not 2^32, which is closer to 4 billion).

You're right. I wrote that 2^33 in haste without thinking too much about it.

Actually, 2^33 would be closer to the 10 billion/milliard number, if that was the referent.

How did the 9 factors of five magicly run away and 24 extra twos take their place?

Where'd you get the *4* billion? Last I heard there are 6 billion people on Earth. However, he did say "guy", so that should cut it to roughly 3 billion. Then again, there was a "lived around the year" in that phrase, so I guess he could've meant any man who ever lived, which could easily amount to more than a hundred billion people...
Could you try to be a little bit more specific George? :P

Well, technically, :) he said that it was invented by a guy who lived in a country, and there haven't been 100 billion men alive since the emergence of national boundaries, if at all.

Most estimates give around 12,000,000,000 (that way we do not have to worry about its name) people total (I am not sure if that is only recorded history), so only about half of that many, or 6,000,000,000, could possibly have been the referent. "4 billion," assuming an American decimal billion (10^9), is not too far off.

Um...maybe you misunderstood me. What I meant is that I entered "e^(pi*i)+1" into my calc and when the result came up, I picked the correct option on the survey.

Maybe its just becuase I'm on the math team at school, but it strikes me as funny that on a site of geeks, most had to resort to a calculator to tell them the answer to the greatest equation in math. Anyways many of you need a lesson so click copy the link below ignoring spaces (you know the deal)

http://www.math.toronto.edu /mathnet/questionCorner /epii.html

I knew it was 0 but almost picked 0! untill my brother told me that was 1.

That link has a great explanation, thanks for posting it. I'd only seen the proof by De Moivre's formula before.