They're two dimensional vectors, but we can extend it to an arbitrary number of dimensions.

Our world was cyclic if you fell off one end you would continue at the other end.

In time you will learn to see what is extra dimensional with as much clarity as you learn to see the physical dimension.

An analogy would be if you had an 8 meter by 8 meter room, how much carpeting would you need is kind of the size of the space you need to fill out in two dimensions on some type of surface.

So now I'm going to show you a number of projects that we've built, from one dimensional, two dimensional, three dimensional and even four dimensional systems.

But the convention for vectors is that you can start at any point.

Beyond it is another dimension a dimension of sound... a dimension of sight... a dimension of mind.

Then we definitely have one or more digits, 867, 3, 1.

An we'll see that it keeps cycling back.

And stack can mean this way, or it can mean this way, or it can mean in some arbitrary n dimensional space.

Here js stands for JavaScript, and this is the text of the program.

Let's say that a hypersphere is the 4D equivalent of a 3D sphere.

B goes straight up and down, so we can add up arbitrary multiples of b to that.

And so on. To render means to create an image.

Galaxies seem to fit all over this particular family of profiles.

Any

For any given price, it's going to lower the quantity demanded.

It could be 1 2, it could be 10.

We said this could be any constant and this could be any constant.

If we want to say there's no dirt in any location, it's a little bit more complicated.

sort of... a portal between this reality and the next.

And what we calculated here is just the average slope across this change in time.

I mean, we don't know what they are.

All the other values should be zero.

Random engine

Random colors

Random Lamp Style

Any files

Any kind of value

Jeeves, Mr. Bickersteth is still up the pole.

Any raccoon.

It doesn't work in a universe with four dimensions of space, nor five, nor six.

They used Harris corner detectors to find corners in the image of this toy 3D house, and they were able from a number of images to fully recover the 3D structure of every single corner point, as shown in this video.

Now when we talk about a three dimensional surface it's a three dimensional surface of a four dimensional sphere that means that any of the three dimensions that are over here on the surface, I can only draw two but that means, if this is true, if the Universe is a three dimensional surface of a four dimensional sphere, that means if you go up and if you just keep going up, you'll eventually come back from the bottom.

If you take the intersection of that plane and that cone and in future videos, and you don't do this in your algebra two class.

Now our domain is the xy plane.

You guys have been great, but this is my mess.

Well this guy is just the dot product of this with itself.

And the way I want you to get there is through a programming exercise.

If you take a pin hole camera you can position the pin hole itself anywhere.

Your next assignment.

Six random colors

Two random colors

Random text alignment

anything