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In the 1770s Euler discovered an infinite family of triangles
with three rational sides and three rational medians---however, 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