QR code stands for quick response code, and it's a two dimensional bar code that holds a good deal more information than a traditional bar code.

A two dimensional vector is needed

It's a thin film, two dimensional existence.

You might think paper is two dimensional.

We have progressed from a zero dimensional point, to a one dimensional line segment, to a two dimensional triangle.

So next, we will talk about two dimensional and three dimensional shapes of ellipticals.

So you can basically program any three dimensional shape or one dimensional, two dimensional up into this chain completely passively.

Let's say we're dealing with two dimensional vectors.

But what if our world were two dimensional?

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.

These two molecules code and decode.

A two dimensional space is defined by two perpendicular lines, which describe a flat plane

The value function itself is 3 dimensional, and here is the code that I've been using.

And we're also translating that into two dimensional systems so flat sheets that can self fold into three dimensional structures.

Now to look at the code, I'm just going to code those two conditions.

Finally, even though these yi's and xi's are two dimensional vectors, when you implement your code, it may be easier to just iterate over each individual entry.

Two dimensional surfaces are usually as far as we need to go.

So this isn't too different from the two dimensional problem so far.

like a 4 dimensional or 5 dimensional figure.

Welcome back.What should these two lines of code print?

I turn them into two and three dimensional pieces and sculptures and installations.

They then discovered that two dimensional engravings on clay tablets were even simpler.

Which is, what happens if these two, three dimensional worlds should actually collide?

So this wall is being reinforced by a two dimensional mesh of steel.

In fact, after I wrote the final code, about two thirds of that code is from homeworks.

Scientists have created metamaterials to guide rays of light around tiny, two dimensional objects.

So if we move back, this is a two dimensional typical tree of life.

A square meter is a two dimensional measurement, that's 1 meter on each side.

But for area we got square meters, because we're counting these two dimensional measurements.

So just like the two dimensional problem, you're only allowed to make forward progress.

How many lines of code are there? About two million.

A two dimensional vector, you could represent like x1, x2, kind of like a coordinate.

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

Sorting multi dimensional array

Insert 2 dimensional vector

Toward the Dimensional Gate.

This is all effectively the same code as we had before when we did dynamic programming in a 2 dimensional world.

Remember that now this state space is 3 dimensional, not 2 dimensional.

And basically, the concept is, how do you represent the three dimensional image of the night sky that surrounds us onto a flat, portable, two dimensional surface.

And now if you watched the two dimensional path counting brain teaser, you know that there's two ways to get here.

However, I printed out a 2 dimensional table, not a 3 dimensional table.

And the resources we use are not this two dimensional swath of land that we have.

Now, if you recall, each layer is actually a large two dimensional grid of tile data.

A seat works in a two dimensional world, where gravity blasts down on that seat, OK?

So matrix is just another way for saying, is a 2D or a two dimensional array.