Xref: utzoo comp.theory.dynamic-sys:190 sci.math:15795 sci.physics:17526
Path: 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

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