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Re: e^(pi*i) + 1 != 0!
Peter Wakefield  Account Info

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

Reply to this comment    16 May 2005, 19:40 GMT


Re: Re: e^(pi*i) + 1 != 0!
korkow Account Info

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'

Reply to this comment    17 May 2005, 00:37 GMT

Re: Re: Re: e^(pi*i) + 1 != 0!
Patrick Stetter  Account Info
(Web Page)

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.

Reply to this comment    17 May 2005, 01:36 GMT


Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Kevin Kofler Account Info
(Web Page)

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

Reply to this comment    17 May 2005, 11:54 GMT


Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Patrick Stetter  Account Info
(Web Page)

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

Reply to this comment    17 May 2005, 20:24 GMT


Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
redsoxfan Account Info

typeo :P

Reply to this comment    18 May 2005, 15:22 GMT


Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Chris Williams  Account Info

tipo.

Reply to this comment    18 May 2005, 19:22 GMT

Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
CajunLuke  Account Info
(Web Page)

typo

Reply to this comment    19 May 2005, 16:37 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
mindstorm23 Account Info

Good gracious...

Reply to this comment    20 May 2005, 03:34 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Lewk Of Serthic  Account Info
(Web Page)

My goodness...

Reply to this comment    21 May 2005, 06:33 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Patrick Stetter  Account Info
(Web Page)

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

Reply to this comment    22 May 2005, 15:55 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Me13579  Account Info

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

Reply to this comment    23 May 2005, 07:36 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
Rug  Account Info

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

Reply to this comment    23 May 2005, 19:56 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 = 0!
db810  Account Info
(Web Page)

What are you programming?

Reply to this comment    24 May 2005, 23:01 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 = 0!
supportthe81 Account Info

You can prograhm?

Reply to this comment    25 May 2008, 01:58 GMT


Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 != 0!
supportthe81 Account Info

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

Reply to this comment    25 May 2008, 02:02 GMT


Re: Re: Re: e^(pi*i) + 1 != 0!
Daniel Bishop  Account Info
(Web Page)

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

Reply to this comment    24 May 2005, 01:46 GMT


Re: Re: Re: Re: e^(pi*i) + 1 != 0!
db810  Account Info
(Web Page)

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

Reply to this comment    24 May 2005, 23:00 GMT

Re: e^(pi*i) + 1 =
JcN  Account Info
(Web Page)

DUH!!!!!

Reply to this comment    16 May 2005, 19:47 GMT


Re: Re: e^(pi*i) + 1 =
burntfuse  Account Info
(Web Page)

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

Reply to this comment    16 May 2005, 20:51 GMT

Re: Re: Re: e^(pi*i) + 1 =
george linkington  Account Info
(Web Page)

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

Reply to this comment    16 May 2005, 20:56 GMT

Re: Re: Re: Re: e^(pi*i) + 1 =
george linkington  Account Info
(Web Page)

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.

Reply to this comment    16 May 2005, 20:59 GMT


Re: Re: Re: Re: Re: e^(pi*i) + 1 =
KermMartian Account Info
(Web Page)

Congratuldations...you just described 4 billion people.

Reply to this comment    17 May 2005, 13:42 GMT

Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
tdavis07  Account Info

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

Reply to this comment    18 May 2005, 01:02 GMT


Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
benryves  Account Info
(Web Page)

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.

Reply to this comment    18 May 2005, 08:47 GMT


Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
redsoxfan Account Info
(Web Page)

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

Reply to this comment    18 May 2005, 15:27 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
benryves  Account Info
(Web Page)

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

Reply to this comment    18 May 2005, 17:48 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Chris Williams  Account Info

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

Reply to this comment    18 May 2005, 19:22 GMT

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
redsoxfan Account Info

10^9

Reply to this comment    19 May 2005, 12:32 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Chris Williams  Account Info

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

Reply to this comment    19 May 2005, 19:14 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Zeroko  Account Info
(Web Page)

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

Reply to this comment    19 May 2005, 14:12 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Chris Williams  Account Info

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

Reply to this comment    19 May 2005, 19:14 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Zeroko  Account Info
(Web Page)

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

Reply to this comment    19 May 2005, 23:43 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
db810  Account Info
(Web Page)

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

Reply to this comment    24 May 2005, 23:06 GMT


Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Rob van Wijk  Account Info

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

Reply to this comment    18 May 2005, 01:03 GMT


Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
redsoxfan Account Info

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.

Reply to this comment    18 May 2005, 15:32 GMT


Re: Re: Re: Re: Re: Re: Re: Re: e^(pi*i) + 1 =
Zeroko  Account Info
(Web Page)

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.

Reply to this comment    19 May 2005, 23:42 GMT


Re: Re: Re: Re: e^(pi*i) + 1 =
burntfuse  Account Info
(Web Page)

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.

Reply to this comment    18 May 2005, 00:28 GMT


E^PI I=-1 !!!!
Patrick Stetter  Account Info
(Web Page)

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

Reply to this comment    16 May 2005, 23:17 GMT

Re: E^PI I=-1 !!!!
Jerk  Account Info

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

Reply to this comment    17 May 2005, 23:10 GMT


Re: E^PI I=-1 !!!!
no_one_2000_  Account Info
(Web Page)

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

Reply to this comment    18 May 2005, 21:41 GMT

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