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From: ljdickey@watmath.UUCP (Lee Dickey)
Newsgroups: net.math
Subject: Re: more about e (kinda') - (nf)
Message-ID: <8274@watmath.UUCP>
Date: Mon, 9-Jul-84 14:01:42 EDT
Article-I.D.: watmath.8274
Posted: Mon Jul  9 14:01:42 1984
Date-Received: Tue, 10-Jul-84 00:30:11 EDT
References: <282@ihlpf.UUCP>
Organization: U of Waterloo, Ontario
Lines: 19

I think that identity is really neat too...  I like to
write it in another way...

        0 = 1 + e ** ( i * pi )

Then in addition to the three heavies you mentioned, there are 
two more, namely 0 and 1.
But also, notice that there are 4 other heavies in there too...
addition, multiplication, exponentiation, and equality.
This identity falls out of Euler's Formula, which comes from 
the definitions of the power series for exp(x), sin(x), and cos(x).  
If you can remember the first series, you can recall the other two
by plugging in    i*t   and sorting out the  i  parts.  Of course
I have to look carefully at what convergence of complex power
series means before I find the "proof" convincing, but the formal
manipulation is easy and entertaining.
-- 
  Lee Dickey, University of Waterloo.  (ljdickey@watmath.UUCP)
 	... {allegra, decvax} !watmath!ljdickey