This question is a generalisation of the 3D space question asked a few days ago: 3D SPACE - RATIONAL DISTANCE
Of course, the points must not belong to the same hyperplane.
Asked
Active
Viewed 60 times
1
Edouard L.
- 581
1 Answers
2
The thread already gives you he answer. Just construct the infinite family in the unitary circle of the plane (say, using the first coordinates), then join the points of the form $\sqrt{8} e_j $ for $j \geq 3$. Interesting generalization though, it's nice to know that there is such set out there.
PenasRaul
- 1,224
-
Two of those $\sqrt3 e_j$ points would have a mutual distance of $\sqrt6$ -- hardly rational. – hmakholm left over Monica Oct 24 '16 at 08:11
-
I was using $\sqrt{8} $ in the computations but forgot to change that into the actual answer, sorry for that. Answer edited. – PenasRaul Oct 24 '16 at 08:21