Article View: comp.theory.dynamic-sys
Article #146Continued fractions (was square roots by hand or computer)
From: Jeff Erickson
Date: Fri, 15 Mar 1991 20:58
Date: Fri, 15 Mar 1991 20:58
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rthomson@mesa.dsd.es.com (Rich Thomson) writes: | I think it turns out that non-rational numbers have a continued | fraction expansion that is eventually periodic (i.e. after a finite | number of coefficients in the expansion, a block of coefficients | repeats infinitely), while all rational numbers have a finite | continued fraction expansion. Only (and all) roots of quadratic equations have periodic continued fraction expansions. Numbers like 2^(1/3), log(2), and pi do not. -- Jeff Erickson \ My dish of love is overflows, jeff@ics.uci.edu \ and I'm a heppy, heppy ket! jeff@128.195.1.1 \ -- Krazy Kat
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Path: arc1-ca.pugleaf.net!utzoo!news-server.csri.toronto.edu!cs.utexas.edu!usc!orion.oac.uci.edu!ucivax!jeff From: jeff@ics.uci.edu (Jeff Erickson) Newsgroups: comp.theory.dynamic-sys,sci.math,sci.physics Subject: Continued fractions (was square roots by hand or computer) Message-ID: <27E1355C.22618@ics.uci.edu> Date: 15 Mar 91 20:58:04 GMT References: <1991Feb28.220523.6184@zaphod.mps.ohio-state.edu> <1991Mar1.001103.6341@cec1.wustl.edu> <1991Mar14.113902.97@bsu-ucs.uucp> <1991Mar15.063023.6605@dsd.es.com> Organization: UC Irvine Department of ICS Lines: 15