Here are some papers supporting a recent preprint "Rational Triangles with Equal Area" recently accepted by the New York Journal of Mathematics. You may retrieve the AMS-TeX source, (which requires the journal's style file), or the DVI and PostScript versions of the paper. Note that there is an Xfig figure, a PostScript version of which is included at one point, and which you must import separately in any of those versions except the PostScript form of the paper itself. (That is, you may either retrieve only the .ps file and view it with your PostScript reader, or you must retrieve figure1.ps along with either the .tex or .dvi file, and process as you prefer.) I also put here the Maple V input source code for verifying the formulas used in the paper.

Here is the abstract of the paper.

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.