
In the 1770s Euler discovered an infinite family of triangles
with three rational sides and three rational medianshowever, this
family did not contain all such triangles. Over 200 years later, Buchholz and Hayes found
a parameterisation of all rational sided triangles with two rational
medians. When one tries to force all of these triangles to have a
third rational median one is forced to find rational points on an
elliptic surface. For more details see Triangles with 3 rational medians. 
Ralph Buchholz
27 March 2001