diff --git a/.ipynb_checkpoints/Apollonian Circle Packings-checkpoint.ipynb b/.ipynb_checkpoints/Apollonian Circle Packings-checkpoint.ipynb
index 40bfa46..d6c06f7 100644
--- a/.ipynb_checkpoints/Apollonian Circle Packings-checkpoint.ipynb	
+++ b/.ipynb_checkpoints/Apollonian Circle Packings-checkpoint.ipynb	
@@ -998,7 +998,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I'm not sure if this works or not. I suspect that it is highly dependent on the order of the circles in the root. Interestingly, it looks like the only relation it was able to deduce for the tetrahedral packing is $b_1, b_2, b_3, b_4 = 0$, meaning there is no null space, as we'd expect. The octahedral quadratic form we get is very different, which isn't surprising, I guess, since this is a very different coordinate system, but I'm not sure if it's right. Likewise, for some reason, we get the cubical quadratic form from the root tetrahedral packing, which doesn't make sense. For whatever reason, though, we get the right matrix."
+    "I suspect that it is highly dependent on the order of the circles in the root. Interestingly, it looks like the only relation it was able to deduce for the tetrahedral packing is $b_1, b_2, b_3, b_4 = 0$, meaning there is no null space, as we'd expect. The octahedral quadratic form we get is very different, which isn't surprising, I guess, since this is a very different coordinate system, but I'm not sure if it's right. It feels very strange, since it's only really two dimensional, rather than four, and it doesn't quite look like the equations hold up. But it does absolutely work for the tetrahedral packing, which is awesome."
    ]
   }
  ],
diff --git a/Apollonian Circle Packings.ipynb b/Apollonian Circle Packings.ipynb
index 40bfa46..d6c06f7 100644
--- a/Apollonian Circle Packings.ipynb	
+++ b/Apollonian Circle Packings.ipynb	
@@ -998,7 +998,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I'm not sure if this works or not. I suspect that it is highly dependent on the order of the circles in the root. Interestingly, it looks like the only relation it was able to deduce for the tetrahedral packing is $b_1, b_2, b_3, b_4 = 0$, meaning there is no null space, as we'd expect. The octahedral quadratic form we get is very different, which isn't surprising, I guess, since this is a very different coordinate system, but I'm not sure if it's right. Likewise, for some reason, we get the cubical quadratic form from the root tetrahedral packing, which doesn't make sense. For whatever reason, though, we get the right matrix."
+    "I suspect that it is highly dependent on the order of the circles in the root. Interestingly, it looks like the only relation it was able to deduce for the tetrahedral packing is $b_1, b_2, b_3, b_4 = 0$, meaning there is no null space, as we'd expect. The octahedral quadratic form we get is very different, which isn't surprising, I guess, since this is a very different coordinate system, but I'm not sure if it's right. It feels very strange, since it's only really two dimensional, rather than four, and it doesn't quite look like the equations hold up. But it does absolutely work for the tetrahedral packing, which is awesome."
    ]
   }
  ],