18 May
2016
18 May
'16
3:42 p.m.
On Wed, May 18, 2016 at 4:32 PM, William R Somsky <wrsomsky@gmail.com> wrote:
Are you only considering points w/ rational coordinates?
Consider the squares of the distances: x^2+y^2, (x-1)^2+y^2, and x^2+((y-1)^2). All of these need to be rational, so the differences 2x-1 and 2 y-1 are also rational. Therefore, all triples have rational coordinates. I think this is problem D23 in Guy. R. K. Guy, "Rational Distances from the Corner of a Square." Dunno is anyone has noticed that ellipse before.