  We provide a general framework to construct colorings avoiding short
monochromatic arithmetic progressions in Euclidean Ramsey theory. Specifically,
if $\ell_m$ denotes $m$ collinear points with consecutive points of distance
one apart, we say that $\mathbb{E}^n \not \to (\ell_r,\ell_s)$ if there is a
red/blue coloring of $n$-dimensional Euclidean space that avoids red congruent
copies of $\ell_r$ and blue congruent copies of $\ell_s$. We show that
$\mathbb{E}^n \not \to (\ell_3, \ell_{20})$, improving the best-known result
$\mathbb{E}^n \not \to (\ell_3, \ell_{1177})$ by F\"uhrer and T\'oth, and also
establish $\mathbb{E}^n \not \to (\ell_4, \ell_{18})$ and $\mathbb{E}^n \not
\to (\ell_5, \ell_{10})$ in the spirit of the classical result $\mathbb{E}^n
\not \to (\ell_6, \ell_{6})$ due to Erd{\H{o}}s et. al. We also show a number
of similar $3$-coloring results, as well as $\mathbb{E}^n \not \to (\ell_3,
\alpha\ell_{6889})$, where $\alpha$ is an arbitrary positive real number. This
final result answers a question of F\"uhrer and T\'oth in the positive.
