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Offline syhprum

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How does this compute
« on: 18/12/2011 18:51:31 »
e^i pi = -1 how does this come about


 

Offline imatfaal

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Re: How does this compute
« Reply #1 on: 19/12/2011 10:38:20 »
In simplistic terms because if you plug 366f4a79709a54a95ad8cdf9627a50a4.gif into Euler's Formula the answer is -1

Euler's formula states that

dc21edcc2c28ec0679529b3915ba345a.gif

as e01b00c11ffe142d251110fda00f5722.gif and a518f3ed2896866debba53d4b21312f2.gif then ac7400fae2d51676e60c51d5507ac6aa.gif

It can be demonstrated by using infinite series representations of both sides and showing they are equal. 

The actual "how it comes about" for Euler's formula is difficult - but you could think of the two sides of dc21edcc2c28ec0679529b3915ba345a.gif  in terms of unit circles.  813b66034b909cb6a3df8a1faad8b414.gif traces a unit circle of circumference ddb170bfa1ac6a375cf38761fe9c6f48.gif radians on the real number plane and conversely db7b57ceb4fef7805bf10a04046a1a9a.gif could be said to trace a unit circle on the complex number plane as x varies through real numbers
 

Offline syhprum

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Re: How does this compute
« Reply #2 on: 19/12/2011 20:36:07 »
I found it rather puzzling at first as to why the answer did not contain any imaginary parts but when I found out sin/cos functions were iinvolved that can take any value between +1 to -1 including zero all became clear

P.s wheres the spell checker ?
 

Offline Don_1

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Re: How does this compute
« Reply #3 on: 22/12/2011 08:00:37 »
366f4a79709a54a95ad8cdf9627a50a4.gif into Euler's Formula the answer is -1

Euler's formula states that

dc21edcc2c28ec0679529b3915ba345a.gif

as e01b00c11ffe142d251110fda00f5722.gif and a518f3ed2896866debba53d4b21312f2.gif then ac7400fae2d51676e60c51d5507ac6aa.gif
Euler's formula
dc21edcc2c28ec0679529b3915ba345a.gif 
813b66034b909cb6a3df8a1faad8b414.gif
ddb170bfa1ac6a375cf38761fe9c6f48.gif
conversely db7b57ceb4fef7805bf10a04046a1a9a.gif




P.s wheres the spell checker ?


Spell checker!!! Never mind the spell checker, where's the algebra checker???
 

Offline imatfaal

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Re: How does this compute
« Reply #4 on: 22/12/2011 10:09:44 »
Spell checker!!! Never mind the spell checker, where's the algebra checker???

I was very pleased with my pretty new latex euler

on your marks, get set,.... pun!
 

Offline syhprum

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Re: How does this compute
« Reply #5 on: 23/12/2011 19:47:33 »
I have "Wolfram Mathmatica" but little skill in using it and would like to run thru the proof of Eulers  Formula which I find very elegent.
 

Offline Geezer

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Re: How does this compute
« Reply #6 on: 23/12/2011 20:12:55 »
I was very pleased with my pretty new latex euler


Did you get a slide euler?
 

Offline syhprum

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Re: How does this compute
« Reply #7 on: 23/12/2011 20:34:56 »
When my son started technical high school about five years after pocket calculators got common I had to buy him a slide rule !.
I wonder how many companies still use them.
 

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Re: How does this compute
« Reply #7 on: 23/12/2011 20:34:56 »

 

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