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From: robertj@garfield.UUCP (Robert Janes)
Newsgroups: net.math
Subject: Transcendental Pi
Message-ID: <2228@garfield.UUCP>
Date: Mon, 17-Dec-84 16:18:32 EST
Article-I.D.: garfield.2228
Posted: Mon Dec 17 16:18:32 1984
Date-Received: Tue, 18-Dec-84 10:45:43 EST
Distribution: net
Organization: Memorial U. of Nfld. C.S. Dept., St. John's
Lines: 33

n upon the irrationality of Pi brings to
	mind a further fact relevant to this number.Not only is Pi
	irrational but furthermore it is transcendental.That is to
	say that there does not exist a polynomial which has only
	integeral co-efficents having Pi as a root.(It can also be 
	said that Pi is not an algebraic number I believe).

	Another number of this nature is e (euler's number)as well
	as the number 0.110001000..1000..010.. which has 0's in every
	place except the k!th place where k is an integer.I would 
	appreciate two things:

		1.Refences to the proof of the proof of the transcendentality
		  of Pi.

		2.References to any other interesting transcendental
		  numbers.(I'm told that the cardinality of the transcendentals
		  is the same as that of the reals so please do not send
		  any old example,just interesting ones(what ever that may
		  be)).

	Please send by mail!

	I'm also told that the fact that Pi is transcendental makes the old
	problem of constructing a square with the same area as a given 
	circle using only a straightedge and ruler impossible.An explan-
	ation of why this is so would be welcome.

	I stand to be corrected on any of the above statements.

Thanks:Robert Janes
       Memorial University of Newfoundland.