ctb@ihlpf.UUCP (baumer, c.t.) (07/08/84)
#N:ihlpf:6200023:000:1033 ihlpf!ctb Jul 7 12:45:00 1984 . ah, you beat me to it, barryw. i also dug out asimov on numbers. i hadn't read it in years. i just wanted to throw in an extra comment that the book deals with all kinds of interesting 'number' stuff - pi, factorials, fibonacci series, googleplex, calendars etc. etc. your average person would look at the above examples and say 'i know all that junk'. true, but there's a LOT more. it goes into the history behind various numbers, calendars, etc. almost treating them like subjects of a biography. it's more than just the math, it's all the interesting stuff and personalities surrounding the math, too! asimov is GREAT at mixing entertainment AND learning. for example, when i was first reading asimov on numbers, (in high school) i didn't know e**(pi * i) = -1 little tidbits like that are fun to run across. what an interesting relationship between three pretty big heavyweights (as far as numbers go :-), e, pi, and i! ron (replies to: ihnp4!ihdev!rjv) ps: anyone want to prove the above equality?
ljdickey@watmath.UUCP (Lee Dickey) (07/09/84)
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