Mordell proved that every quadrilateral in the Euclidean plane is arbitrarily close to a quadrilateral whose sides and diagonals are rational. What if we take five points in the plane? Is there a choice of 5 bad points so that for some positive epsilon, whenever the points are moved at most distance epsilon then two of them are at irrational distance?
Asked
Active
Viewed 72 times
1
-
1Also posted to MO, https://mathoverflow.net/questions/342018/mordells-theorem-on-rational-quadrilaterals without any notice to either site. Peter, that's an abuse of the system. – Gerry Myerson Sep 19 '19 at 23:15
-
My apologies. I did not intend any offence. – Peter Kropholler Sep 28 '19 at 17:28