Old 03-14-2006, 11:43 AM   #1
deltro300111
FFR Player
 
deltro300111's Avatar
 
Join Date: Aug 2003
Location: d colon
Age: 31
Posts: 1,014
Send a message via AIM to deltro300111 Send a message via MSN to deltro300111 Send a message via Yahoo to deltro300111
Default Anyone know why this works?

pi = ln(-e)-1/sqrt(-1)

The original equation is

ln(-e) = 1 + (pi)i

I just isolated pi.
__________________
deltro300111 is offline   Reply With Quote
Old 03-14-2006, 12:30 PM   #2
Tasselfoot
Retired BOSS
Retired StaffFFR Simfile AuthorFFR Veteran
 
Tasselfoot's Avatar
 
Join Date: Jul 2003
Location: Widget Heaven
Age: 36
Posts: 25,184
Send a message via AIM to Tasselfoot Send a message via MSN to Tasselfoot Send a message via Skype™ to Tasselfoot
Default Re: Anyone know why this works?

Yes. I know why.
__________________
RIP
Tasselfoot is offline   Reply With Quote
Old 03-14-2006, 01:24 PM   #3
aperson
FFR Hall of Fame
Retired StaffFFR Simfile AuthorFFR Veteran
 
aperson's Avatar
 
Join Date: Jul 2003
Location: Houston
Posts: 3,298
Send a message via AIM to aperson
Default Re: Anyone know why this works?

You're just rearranging Euler's identity with some added terms:

__________________
aperson is offline   Reply With Quote
Old 03-14-2006, 01:27 PM   #4
talisman
Resident Penguin
FFR Simfile AuthorFFR Veteran
 
talisman's Avatar
 
Join Date: May 2003
Age: 34
Posts: 4,598
Send a message via AIM to talisman
Default Re: Anyone know why this works?

I just typed the same thing as ap but vb swallowed it...

and that identity comes from some Calc II nonsense I believe, with series and whatnot.
talisman is offline   Reply With Quote
Old 03-14-2006, 01:35 PM   #5
XXXsmittyXXX
Anxiety monster
FFR Veteran
 
XXXsmittyXXX's Avatar
 
Join Date: Jul 2005
Location: Yorktown, VA
Age: 32
Posts: 6,924
Send a message via AIM to XXXsmittyXXX Send a message via Skype™ to XXXsmittyXXX
Default Re: Anyone know why this works?

damn smart ****s
__________________
XXXsmittyXXX is offline   Reply With Quote
Old 03-14-2006, 01:49 PM   #6
aperson
FFR Hall of Fame
Retired StaffFFR Simfile AuthorFFR Veteran
 
aperson's Avatar
 
Join Date: Jul 2003
Location: Houston
Posts: 3,298
Send a message via AIM to aperson
Default Re: Anyone know why this works?

Quote:
Originally Posted by talisman
I just typed the same thing as ap but vb swallowed it...

and that identity comes from some Calc II nonsense I believe, with series and whatnot.


It's generally known as Euler's formula. I think you can prove it with Calc II series, but the first application I've seen of it was solving 2nd order linear ODEs that have complex conjugates as answers.
__________________
aperson is offline   Reply With Quote
Old 03-14-2006, 01:57 PM   #7
Kefit
FFR Player
 
Kefit's Avatar
 
Join Date: Apr 2003
Posts: 1,517
Send a message via AIM to Kefit
Default Re: Anyone know why this works?

Oh hey this topic came up almost a year ago.

Quote:
Originally Posted by Kefit, a year or so ago
This equation is incredibly important to physics and differential equations. Lemme see if I can remember the proof:

First off, this proof uses infinite series. Put basically, any differentiable function can be represented by the sum of an infinite series. No, I don't expect you to know what that means. Just accept that:

cos(x) = 1 - (x^2)/(2!) + (x^4)/(4!) - (x^6)/(6!) + . . .

sin(x) = x - (x^3)/(3!) + (x^5)/(5!) - (x^7)/(7!) + . . .

e^x = 1 + x + (x^2)/(2!) + (x^3)/(3!) + . . .

It follows that:

e^(i*x) = 1 + (i*x) - (x^2)/(2!) - (i*x^3)/(3!) + (x^4)/(4!) + (i*x^5)/(5!) - (x^6)/(6!) + . . .

i*sin(x) = (i*x) - (i*x^3)/(3!) + (i*x^5)/(5!) - (i*x^7)/(7!) + . . .

Now something interesting happens when you add cos(x) and i*sin(x) together. Lemme see if I can illustrate this clearly:

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

Don't be discouraged if the idea of infinite series is unfamiliar to you - just take the series I gave for sin(x), cos(x), and e^x for granted, and everything else I show above follows from simple arithmetic on the series.

Anyway, this creates the general equation:

e^(i*x) = cos(x) + i*sin(x)

if x = PI, then:

e^(i*PI) = cos(PI) + i*sin(PI) = -1 + i*0 = -1
Shame on you ap for not being familiar with this.
__________________


Quote:
Originally Posted by seinno
and also thank you everone for clearing it up for me I will try to start using my two hands iv tried quit a bit i put my left hand index and middle finger middle finger is on the up arrow index on on left arrow and right hand i use my index for the down button and middle for the right button does that seem weird?
Kefit is offline   Reply With Quote
Old 03-14-2006, 04:31 PM   #8
Kilgamayan
Super Scooter Happy
FFR Simfile Author
 
Kilgamayan's Avatar
 
Join Date: Feb 2003
Location: Location, Location.
Age: 36
Posts: 6,584
Send a message via AIM to Kilgamayan
Default Re: Anyone know why this works?

Shame on me for not being familiar with that too.
__________________
I watched clouds awobbly from the floor o' that kayak. Souls cross ages like clouds cross skies, an' tho' a cloud's shape nor hue nor size don't stay the same, it's still a cloud an' so is a soul. Who can say where the cloud's blowed from or who the soul'll be 'morrow? Only Sonmi the east an' the west an' the compass an' the atlas, yay, only the atlas o' clouds.
Kilgamayan is offline   Reply With Quote
Old 03-14-2006, 09:40 PM   #9
deltro300111
FFR Player
 
deltro300111's Avatar
 
Join Date: Aug 2003
Location: d colon
Age: 31
Posts: 1,014
Send a message via AIM to deltro300111 Send a message via MSN to deltro300111 Send a message via Yahoo to deltro300111
Default Re: Anyone know why this works?

this all came out when I was taking an Algebra II test, and trying to find one of the ever prevalent patterns. I plugged in ln(-e), and realized that the calculator spat out pi(i)+1, and I was like, "what the hell", and I tried to isolate e, but lacked the mad skills to do so. I know from where e is derived but never knew why.
__________________
deltro300111 is offline   Reply With Quote
Old 03-14-2006, 11:12 PM   #10
GuidoHunter
is against custom titles
FFR Veteran
 
GuidoHunter's Avatar
 
Join Date: Oct 2003
Location: Texas
Age: 36
Posts: 7,379
Send a message via AIM to GuidoHunter Send a message via Skype™ to GuidoHunter
Default Re: Anyone know why this works?

They didn't teach you what the log function looked like in Algebra II? What the hell were you trying to do taking the natural log of a negative number?

--Guido

http://andy.mikee385.com
__________________

Quote:
Originally Posted by Grandiagod View Post
Quote:
Originally Posted by Grandiagod View Post
She has an asshole, in other pics you can see a diaper taped to her dead twin's back.
Sentences I thought I never would have to type.
GuidoHunter is offline   Reply With Quote
Old 03-15-2006, 12:10 AM   #11
aperson
FFR Hall of Fame
Retired StaffFFR Simfile AuthorFFR Veteran
 
aperson's Avatar
 
Join Date: Jul 2003
Location: Houston
Posts: 3,298
Send a message via AIM to aperson
Default Re: Anyone know why this works?

Quote:
Originally Posted by GuidoHunter
They didn't teach you what the log function looked like in Algebra II? What the hell were you trying to do taking the natural log of a negative number?

--Guido

http://andy.mikee385.com
I take it you've never heard of the complex coordinate plane have you.
__________________
aperson is offline   Reply With Quote
Old 03-15-2006, 12:31 AM   #12
GuidoHunter
is against custom titles
FFR Veteran
 
GuidoHunter's Avatar
 
Join Date: Oct 2003
Location: Texas
Age: 36
Posts: 7,379
Send a message via AIM to GuidoHunter Send a message via Skype™ to GuidoHunter
Default Re: Anyone know why this works?

Funny, as I'm taking Functions of Complex Variables right now. Very cute.

Note how he's in algebra II. Also note that I said natural log. I am well aware that there are an infinite number of solutions to log(-x) for any x, and how log and Log mean very different things.

--Guido

http://andy.mikee385.com
__________________

Quote:
Originally Posted by Grandiagod View Post
Quote:
Originally Posted by Grandiagod View Post
She has an asshole, in other pics you can see a diaper taped to her dead twin's back.
Sentences I thought I never would have to type.
GuidoHunter is offline   Reply With Quote
Old 03-15-2006, 01:01 AM   #13
aperson
FFR Hall of Fame
Retired StaffFFR Simfile AuthorFFR Veteran
 
aperson's Avatar
 
Join Date: Jul 2003
Location: Houston
Posts: 3,298
Send a message via AIM to aperson
Default Re: Anyone know why this works?

I definitely did complex logarithms in my algebra II class.

Although I didn't see them again until differential equations
__________________
aperson is offline   Reply With Quote
Old 03-15-2006, 01:52 AM   #14
stealthkidd
Above and Beyond
FFR Veteran
 
stealthkidd's Avatar
 
Join Date: Nov 2005
Location: Toronto
Posts: 368
Default Re: Anyone know why this works?

HOLY CRAP!!! aperson u should get a new section for aperson's insanly hard questions becasue everyone under 18 or so has no ****ing clue wtf ur saying but ppl like it. this is because urs are mostly harder
stealthkidd is offline   Reply With Quote
Old 03-15-2006, 01:57 AM   #15
aperson
FFR Hall of Fame
Retired StaffFFR Simfile AuthorFFR Veteran
 
aperson's Avatar
 
Join Date: Jul 2003
Location: Houston
Posts: 3,298
Send a message via AIM to aperson
Default Re: Anyone know why this works?

Quote:
Originally Posted by stealthkidd
HOLY CRAP!!! aperson u should get a new section for aperson's insanly hard questions becasue everyone under 18 or so has no ****ing clue wtf ur saying but ppl like it. this is because urs are mostly harder
I'm 17.
__________________
aperson is offline   Reply With Quote
Old 03-16-2006, 12:38 PM   #16
iggymatrixcounter
FFR Veteran
FFR Veteran
 
iggymatrixcounter's Avatar
 
Join Date: Nov 2003
Location: OH
Age: 33
Posts: 1,924
Send a message via AIM to iggymatrixcounter
Default Re: Anyone know why this works?

ROFL owned.

But I don't remember negative logs in my algebra class. (Maybe I slept that day or something.)
__________________
lastfm
PANDORA
iggymatrixcounter is offline   Reply With Quote
Old 03-16-2006, 05:17 PM   #17
GuidoHunter
is against custom titles
FFR Veteran
 
GuidoHunter's Avatar
 
Join Date: Oct 2003
Location: Texas
Age: 36
Posts: 7,379
Send a message via AIM to GuidoHunter Send a message via Skype™ to GuidoHunter
Default Re: Anyone know why this works?

No, I'm pretty sure studying complex algebra in algebra II isn't a normal thing.

All we ever did was know a little about complex roots of polynomials. We never got into anything in the real-complex plane, branch cutting, or anything like that.

--Guido

http://andy.mikee385.com
__________________

Quote:
Originally Posted by Grandiagod View Post
Quote:
Originally Posted by Grandiagod View Post
She has an asshole, in other pics you can see a diaper taped to her dead twin's back.
Sentences I thought I never would have to type.
GuidoHunter is offline   Reply With Quote
Old 03-17-2006, 05:01 AM   #18
deltro300111
FFR Player
 
deltro300111's Avatar
 
Join Date: Aug 2003
Location: d colon
Age: 31
Posts: 1,014
Send a message via AIM to deltro300111 Send a message via MSN to deltro300111 Send a message via Yahoo to deltro300111
Default Re: Anyone know why this works?

Quote:
Originally Posted by stealthkidd
HOLY CRAP!!! aperson u should get a new section for aperson's insanly hard questions becasue everyone under 18 or so has no ****ing clue wtf ur saying but ppl like it. this is because urs are mostly harder
YOU ARE COOL BECAUSE YOU ARE STUPID.

Now fµck off. Now that it's out there no one cares.
__________________
deltro300111 is offline   Reply With Quote
Old 03-20-2006, 12:37 AM   #19
flamingspinach
FFR Player
 
flamingspinach's Avatar
 
Join Date: Jan 2006
Posts: 269
Default Re: Anyone know why this works?

I'm probably not noticing something, but aren't you not allowed to rearrange alternating series?

-fs
flamingspinach is offline   Reply With Quote
Old 03-20-2006, 01:39 AM   #20
GuidoHunter
is against custom titles
FFR Veteran
 
GuidoHunter's Avatar
 
Join Date: Oct 2003
Location: Texas
Age: 36
Posts: 7,379
Send a message via AIM to GuidoHunter Send a message via Skype™ to GuidoHunter
Default Re: Anyone know why this works?

What exactly do you mean by rearranging? The terms are all just added, if that's what you're meaning...

--Guido

http://andy.mikee385.com
__________________

Quote:
Originally Posted by Grandiagod View Post
Quote:
Originally Posted by Grandiagod View Post
She has an asshole, in other pics you can see a diaper taped to her dead twin's back.
Sentences I thought I never would have to type.
GuidoHunter is offline   Reply With Quote
Reply


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump



All times are GMT -5. The time now is 11:21 PM.


Powered by vBulletin® Version 3.8.1
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.
Copyright FlashFlashRevolution