Re: mysterious numbers

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Re: mysterious numbers

On Thu, 19 Mar 1998 20:08:42 -0500, "Wes Mininger (pyr)"
<miningw@ELMO.NMC.EDU> wrote:

>well e is a natural number and no one really knows why it is what it is..
Sure they do, it's the result of an infinite series, derived from
continuous growth.

>it just works... Pi is another one that just works.. it is really useful,
>but it is a completely meaningless number if you look at just the digits,
>but taken with everything else it is really powerful.
Well, aren't most numbers that way, just look at the digits, and it's
meaningless?  It's pretty clear why that one works, if you consider
the circumference of a polygon as the number of sides approaches
infinity.

>-1 well I dont know
>whats so mysterious about that...
-1, that's a real handy number.  Multiply anything by -1 and you
change the sign, but that's all.

>unless you mean the cos and sin part...
>thats sort of based on pi so it really shouldnt count...  As for i think
>about it.. a number that by definition cannot exist.. since no square can
>ever equal a negative,
Sure they can.  (2i)^2=-4  (3i)^2=-9, I'm sure you see my drift.
There's an infinite number of squares that equal a negative number.
Numbers times the square root of -1, (i) are of the form x*i and they
are called imaginary numbers.
If you think about it, does any number "exist"?  They whole number
idea and all that comes from it is just an invention of humans.  They
are just ideas, symbols, not something that has material form, like a
tree, cat, or houseboat.

>then the inverse of a squaring must be positive,
>but i = sqrt(-1)  how can you do that?
i is defined as the square root of -1.  Therefore i^2=-1

>well you cant really so we have to
>create them so that things like the quadratic equation can work when it
>wouldnt otherwise.
They are useful in electronics, and a few other places.  Your right, i
makes stuff work, that wouldn't otherwise.

>
>On Thu, 19 Mar 1998, Garvin Cung wrote:
>
>:can someone please help me on this equation?
>:
>:show that e^(i * pi) = -1
>:
>:i get the 4 'mysterious' answers:
>:1. e^(i * pi)
>:2. -1
>:3. cos pi + i sin pi
>:4. -1 + 0i
>:
>:according to my book, they say that this equation combines 4 of the
>:most mysterious numbers of mathematics.
I've always seen that called the equation that combines 4 of the most
important numbers.  Actually, it combines the 5 most important
numbers, the fifth being left off, as it often is.
e^(i * pi) = -1 + 0
That zero, is real important, and so often we just take it for
granted!




tram@humboldt10.com
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