Tyler Cosgrove

And what's like the max number?

Like how do we basically organize those points such that we have the max number of them, right?

No, so you would think that, but I can basically explain why.

So let's kind of like formalize this better.

So we have u of n, right?

And this is basically the largest number of unit distance pairs among n points in the plane.

Okay, so basically like we're thinking about like, how do we solve this naively?

It's like, okay, what if we just take all the points?

We have n points and we just put them in a line and unit distance apart, right?

So it looks something like this.

Right, so for this example we have four points, but it doesn't matter, it's just n. So one, two, three, four, how many pairs are there?

There's three, right?

So basically this scales with n minus one.

So you would have a billion points, and there's nine, nine, nine, nine, whatever, n minus one.

Okay, so now if we put it in a grid, what happens?

So if we have a square grid here, there's nine points here, and then how many pairs are there?

I believe there's 12.

And basically as this number scales up,

It's still linear, so it's 2N.

Basically, if you do a billion points, it's two billion pairs.