Apollonian sphere packing
Have you ever played with marbles or balls and tried to stack them on top of each other? Apollonian sphere packing is kind of like that, but instead of just stacking balls, we're packing them as close together as possible in a big space.
To do this, we start with three balls of the same size, and put them next to each other so they're touching. This is like making a little triangle with the balls.
Now we're going to add another ball to the mix. We pick a spot on the edge of one of the three balls, and put the fourth ball there so that it's still touching all three of the other balls. It kind of looks like a pyramid now, with the three balls on the bottom and the fourth one on top.
We keep doing this, adding more and more balls to the mix. Each new ball we add has to touch all of the other balls that are already there, and we try to put it in the most efficient spot possible so that all the balls are packed as tight as they can be.
Eventually, we end up with this really cool pattern of balls, all packed together really tightly. It looks kind of like a bunch of bubbles or soap foam, but all made out of balls. This is called an Apollonian sphere packing.
Scientists and mathematicians are really interested in Apollonian sphere packings because they can use them to study things like geometry and physics. Plus, they're just really cool to look at!
To do this, we start with three balls of the same size, and put them next to each other so they're touching. This is like making a little triangle with the balls.
Now we're going to add another ball to the mix. We pick a spot on the edge of one of the three balls, and put the fourth ball there so that it's still touching all three of the other balls. It kind of looks like a pyramid now, with the three balls on the bottom and the fourth one on top.
We keep doing this, adding more and more balls to the mix. Each new ball we add has to touch all of the other balls that are already there, and we try to put it in the most efficient spot possible so that all the balls are packed as tight as they can be.
Eventually, we end up with this really cool pattern of balls, all packed together really tightly. It looks kind of like a bunch of bubbles or soap foam, but all made out of balls. This is called an Apollonian sphere packing.
Scientists and mathematicians are really interested in Apollonian sphere packings because they can use them to study things like geometry and physics. Plus, they're just really cool to look at!