On rational triangles via algebraic curves. (English) Zbl 1430.11087

Summary: A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between each family and the set of rational points of an algebraic curve. These algebraic curves are: a curve of genus 0, an elliptic curve and a genus 3 curve. We study the set of rational points on each of these curves and explicitly describe some of its rational points.


11G05 Elliptic curves over global fields
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
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