From: utzoo!decvax!ucbvax!npois!alice!rhm Newsgroups: net.math Title: puzzle Article-I.D.: alice.602 Posted: Fri May 28 22:34:47 1982 Received: Sat May 29 10:07:56 1982 The continued fraction representation of a number x is written as x = (n1, n2, n3, ... ) where n1, etc. are positive integers, and x = n1 + 1/(n2 + 1/(n3 + ... )) A continued fraction that terminates (zero from some point on) represents a rational number. 1. Does the continued fraction rep. of every rational number terminate? If not, does it at least repeat? 2. What are the numbers whose continued fraction rep's repeat? 3. The continued fraction (2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, ... ) seems to equal something like 2.718... Is it possible that this is a simple representation of "e", the base of natural logarithhms, which is a transcendental number? Is it in fact equal to e?