Math Is Fun Forum

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

e^i pi

idk if someone already explained this or not
but someone probly already did
but in thte case that some one didnt
i would like to
one of the buds told me something interesting
he told me that he foudna  flaw on the caclulator that he had heard bout on ze inter of nets
it was taht

and i believed him for a while
and i truly thought it was a flaw
but  i believe in my calcultor more than i do in santa having a beer belly
iso i recently foudn out in study demoive
taht it actually was correct
cuz somewhere some one said taht

and if u plug in pi it will work out to negative
pi radians taht is
not degrees
as i have

vv00t w00t
idk i foudn taht interesting

Last edited by shocamefromebay (2007-07-07 11:56:23)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: e^i pi

It is right, and one of those aspects of mathematics that stops you in your tracks and makes your jaw drop ... how could e, i, π and 1 come together so neatly!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

shocamefromebay

Member

Registered: 2007-05-30

Posts: 103

Re: e^i pi

it does make ur mind twitch for  wihle
but it is interesting
thats why we truly believed taht it was a calculator flaw for sucha  long while

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: e^i pi

how could e, i, π and 1 come together so neatly!

Don't forget 0:

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: e^i pi

I haven't worked much with complex numbers and i don't pretend to be an authority on the subject but... while I thought it was amusing that this turned out to be true when i watched my teacher proove it, i didn't really trust it because it looked like we had taken some properties that had been rigorously developed exclusively for real numbers (infinite series, etc) and suddenly applied it to the imaginaries. I mean, we showed that a real function can be represented term by term as an infinte series (provided it satisfies certain conditions) but never touched imaginaries. Is it always valid to stick imaginary numbers in where reals have been shown to work?

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A logarithm is just a misspelled algorithm.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: e^i pi

mikau, here's my point of view:
In an old clculus book the complex numbers were explained not as numbers from the form a+bi, but as doubles (a,b) with some basic definitions.
For example (a,b) + (c,d) = (a+c,b+d) ect.
With the complex numbers we want to "extend" the reals, but if we have a real function, we may extend it in many ways to complex.
So we may want to preserve some of the properties of the function.
It appears that the taylor expansion is pretty important characteristic of a function (differentiable). Many of the complex-valued functions are defined as a taylor series. We use the same series for the real and the complex function, because it preserves its properties.
But there are of course many functions which are defined over the complex plane by other ways with interesting properties - the zeta function and else.

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IPBLE:  Increasing Performance By Lowering Expectations.

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: e^i pi

cool beans, Krassi!

And your new avatar rocks! Is it a fractal? Its hard to tell.

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A logarithm is just a misspelled algorithm.