  Let $\chi_{\Delta}(\mathbb{R}^{n})$ denote the minimum number of colors
needed to color $\mathbb{R}^{n}$ so that there will not be a monochromatic
equilateral triangle with side length $1$. Using the slice rank method, we
reprove a result of Frankl and Rodl, and show that
$\chi_{\Delta}\left(\mathbb{R}^{n}\right)$ grows exponentially with $n$. This
technique substantially improves upon the best known quantitative lower bounds
for $\chi_{\Delta}\left(\mathbb{R}^{n}\right)$, and we obtain \[
\chi_{\Delta}\left(\mathbb{R}^{n}\right)>(1.01446+o(1))^{n}. \]
