wball/Circle-Packings
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

fixed explanation

Browse source
This commit is contained in:
William Ball 2021-03-12 18:11:52 -08:00
parent 95c3b0d050
commit 495139741f
2 changed files with 2 additions and 2 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

2
.ipynb_checkpoints/Apollonian Circle Packings-checkpoint.ipynb
View file

@ -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."
]
}
],

2
Apollonian Circle Packings.ipynb
View file

@ -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."
]
}
],