Three-term unit arithmetic progression is not Euclidean Ramsey
= Three-term unit arithmetic progression is not Euclidean Ramsey
The collinear set $\{0,1,2\}$ is not a <Euclidean Ramsey set>. In every dimension, coloring $x$ by $\lfloor2\|x\|^2\rfloor$ modulo ten prevents a monochromatic congruent copy; the <parallelogram law> would force the corresponding three integer parts to have a second difference strictly between two and six, which cannot be divisible by ten.