From mark@csc.albany.edu Wed Jan 21 09:10:37 1998
Date: Wed, 21 Jan 1998 01:46:08 -0500
From: Mark Steinberger <mark@csc.albany.edu>
Reply-To: Abstracts from the New York Journal of Mathematics
     <NYJMTH-A@CNSIBM.ALBANY.EDU>
To: NYJMTH-A@CNSIBM.ALBANY.EDU
Subject: Rational Triangles with Equal Area

          New Release from the New York Journal of Mathematics

Title: Rational Triangles with Equal Area

Author: David J. Rusin

Date of Publication: January 21, 1998

Keywords: rational triangles, Heron surfaces, elliptic curves

Subject Classification: 11G05

                             Abstract:

   We consider the set of triangles in the plane with rational sides and
   a given area A. We show there are infinitely many such triangles for
   each possible area A. We also show that infinitely many such triangles
   may be constructed from a given one, all sharing a side of the
   original triangle, unless the original is equilateral. There are three
   families of triangles (including the isosceles ones) for which this
   theorem holds only in a restricted sense; we investigate these
   families in detail.  Our explicit construction of triangles with a
   given area may be viewed as a dynamical system in the plane; we
   consider its features as such.  The proofs combine simple calculation
   with Mazur's characterization of torsion in rational elliptic curves.
   We discuss the isomorphism classes of the elliptic curves involved.


This paper's home page is http://nyjm.albany.edu:8000/j/1998/4-1.html.
It contains links to the various graphical formats of the paper.