Naked Science Forum

Non Life Sciences => Geek Speak => Topic started by: syhprum on 18/12/2011 18:51:31

Title: How does this compute
Post by: syhprum on 18/12/2011 18:51:31

e^i pi = -1 how does this come about

Title: Re: How does this compute
Post by: imatfaal on 19/12/2011 10:38:20

In simplistic terms because if you plug into Euler's Formula the answer is -1

Euler's formula states that



as and then

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   in terms of unit circles.  traces a unit circle of circumference radians on the real number plane and conversely could be said to trace a unit circle on the complex number plane as x varies through real numbers

Title: Re: How does this compute
Post by: syhprum 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 ?

Title: Re: How does this compute
Post by: Don_1 on 22/12/2011 08:00:37

Quote from: imatfaal on 19/12/2011 10:38:20

into Euler's Formula the answer is -1

Euler's formula states that



as and then
Euler's formula
 


conversely

(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fbestsmileys.com%2Fclueless%2F1.gif&hash=ba6e884e2ac18d739c0e89967c82862b)

Quote from: syhprum on 19/12/2011 20:36:07

P.s wheres the spell checker ?

Spell checker!!! Never mind the spell checker, where's the algebra checker??? (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.emofaces.com%2Fen%2Fsmilies%2Fd%2Fdunce-smile.gif&hash=104dc1f5650c431aa2481c913cbec7b5)

Title: Re: How does this compute
Post by: imatfaal on 22/12/2011 10:09:44

Quote from: Don_1 on 22/12/2011 08:00:37

Spell checker!!! Never mind the spell checker, where's the algebra checker??? (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.emofaces.com%2Fen%2Fsmilies%2Fd%2Fdunce-smile.gif&hash=104dc1f5650c431aa2481c913cbec7b5)

I was very pleased with my pretty new latex euler

on your marks, get set,.... pun!

Title: Re: How does this compute
Post by: syhprum 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.

Title: Re: How does this compute
Post by: Geezer on 23/12/2011 20:12:55

Quote from: imatfaal on 22/12/2011 10:09:44

I was very pleased with my pretty new latex euler

Did you get a slide euler?

Title: Re: How does this compute
Post by: syhprum 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.