lie-algebras-and-their-representations

diff --git a/sections/sl2-sl3.tex b/sections/sl2-sl3.tex
@@ -706,7 +706,7 @@ multiple choices the ``weight lying the furthest'' along this direction.
 \end{definition}
 
 The next observation we make is that all others weights of \(V\) must lie in a
-sort of \(\frac{1}{3}\)-plane with corners at \(\lambda\), as shown in
+sort of \(\frac{1}{3}\)-cone with apex at \(\lambda\), as shown in
 \begin{center}
   \begin{tikzpicture}
     \AutoSizeWeightLatticefalse
@@ -756,8 +756,8 @@ down the line -- but instead we would like to focus on the problem of finding
 the weights of \(V\) in the first place.
 
 We'll start out by trying to understand the weights in the boundary of
-\(\frac{1}{3}\)-plane previously drawn. As we've just seen, we can get to other
-weight spaces from \(V_\lambda\) by successively applying \(E_{2 1}\).
+previously drawn cone. As we've just seen, we can get to other weight spaces
+from \(V_\lambda\) by successively applying \(E_{2 1}\).
 \begin{center}
   \begin{tikzpicture}
     \begin{rootSystem}{A}