Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site oliven.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!decwrl!sun!idi!oliven!albert From: albert@oliven.UUCP (LuigiAlberto Piodisavoia) Newsgroups: net.math Subject: Curious problem Message-ID: <743@oliven.UUCP> Date: Thu, 6-Dec-84 17:57:16 EST Article-I.D.: oliven.743 Posted: Thu Dec 6 17:57:16 1984 Date-Received: Sun, 9-Dec-84 02:22:12 EST Organization: Olivetti ATC, Cupertino, Ca Lines: 57 While working on a theoretical physics problem I run into the following mathematical curiosity: Suppose you have two functions of the form y(x) = ax + b sin ( cx + d ) which would look something like this: | | | | | | . | .. . | .. . . .. | .. . .. . .. . | .. . .. . . .. . . | .. ... . . ... . . . . | . .. .. .. . . .. . | . ... . . .. | . . .. | . | ----------------------------------------------------------------------- The obvious possibilities that arise by manipulating the coefficients are: i) the curves never intersect. ii) the curves intersect a finite number of times. iii) the curves intesect an infinite number of times. I am interested in the second case, in other words: QUESTION 1. How many roots does ax + b sin ( cx + d ) = ex + f sin ( gx + h ) have when the coefficients a - h are such that the two curves intersect a finite number of times ? Express your answer in terms of a-h. QUESTION 2. Can you guess what in what field of physics would such equations arise ?