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

So this is my three dimensional plane.

I can associate it with this point in this plane right over here, in this two dimensional plane. so I'll say

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.

I missed the two o'clock plane.

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.

The bad weather delayed the plane for two hours.

We bought our plane tickets two months in advance.

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

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.

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.

Suppose we have a mobile robot that is round and lives on a plane, and it can turn on the spot, but its location is given by a two dimensional coordinate.

Plane

Plane

plane

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.

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.

The plane was delayed for two hours on account of the bad weather.

A curve's a curve, a plane's a plane, and the two won't mix.

Now the intersection of this plane, which is now not orthogonal or it's not perpendicular to the axis of this three dimensional cone.

Sorting multi dimensional array

Insert 2 dimensional vector

Toward the Dimensional Gate.

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

Plane crashes.

Reconnaissance plane.

So, the ground plane fails, which is as it should be because the ground plane is obviously farther away than these two objects.

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.