diff --git a/tikz/koch-snowflake/koch-snowflake.tex b/tikz/koch-snowflake/koch-snowflake.tex
index 9565ebd..4c86f1c 100644
--- a/tikz/koch-snowflake/koch-snowflake.tex
+++ b/tikz/koch-snowflake/koch-snowflake.tex
@@ -10,6 +10,20 @@
 % \draw[fill=gray!10] { { { decorate{ (0,0) -- (3,0) -- (1.5,-3) -- (0,0)}}}};
 % \draw[fill=gray!10] { { decorate{ decorate{ (0,0) -- (3,0) -- (1.5,-3) -- (0,0)}}}};
 % \draw[fill=gray!10] { decorate{ decorate{ decorate{ (0,0) -- (3,0) -- (1.5,-3) -- (0,0)}}}};
-\draw[fill=gray!10] decorate{ decorate{ decorate{ decorate{ (0,0) -- (3,0) -- (1.5,-3) -- (0,0)}}}};
+%\draw[fill=gray!10] decorate{ decorate{ decorate{ decorate{ (0,0) -- (3,0) -- (1.5,-3) -- (0,0)}}}};
+%(0,0) -- (3,0) -- (1.5,-3) -- (0,0) does not form an equilateral triangle, so the Koch curves along (3,0) -- (1.5,-3) and (1.5,-3) -- (0,0) are longer than they should be
+
+%using shifts and rotations makes an equilateral triangle easily without dealing explicitly with any irrational coordinates
+\draw decorate{ decorate{ decorate{ decorate{ (0,0) -- (1,0) }}}};
+\begin{scope}[shift={(1,0)}]
+\begin{scope}[rotate=-120]
+\draw decorate{ decorate{ decorate{ decorate{ (0,0) -- (1,0) }}}};
+\end{scope}
+\end{scope}
+\begin{scope}[shift={(-1,0)}]
+\begin{scope}[rotate around={120:(1,0)}]
+\draw decorate{ decorate{ decorate{ decorate{ (0,0) -- (1,0) }}}};
+\end{scope}
+\end{scope}
 \end{tikzpicture}
 \end{document}