Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 GARFIELD 20/11/84; site garfield.UUCP Path: utzoo!utcsrgv!garfield!robertj 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.