4 problems

Let $a,b$ be coprime positive integers with $a\not\equiv b\pmod{3}$, and let $T(a,b,a+b)$ be the degenerate triangle with side parameters $a$, $b$, and $a+b$. Write…

Let $T$ be a triangle, and let $\chi(\mathbb{R}^2,T)$ be the minimum number of colors needed to color the Euclidean plane so that no isometric copy of $T$ is monochromatic. Graham'…

Let $T$ be a triangle, and let $\chi(\mathbb{R}^2,T)$ be the minimum number of colors needed to color the Euclidean plane so that no isometric copy of $T$ is monochromatic. Erdős e…

For a positive integer $c$, let $M_3(c,s)$ be the least integer such that every set of at least $M_3(c,s)$ points in the plane, with no three collinear and colored with $c$ colors,…