# The Naked Scientists Forum

### Author Topic: How does this compute  (Read 2044 times)

#### 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

#### 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 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

#### 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 ?

#### Don_1

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

Euler's formula states that

as and then
Euler's formula

conversely

P.s wheres the spell checker ?

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

#### 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!

#### 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.

#### 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?

#### 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.

#### The Naked Scientists Forum

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