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.

We take this curved 12 dimensional space and transform it into a flat four dimensional space.

And that four dimensional space consists of X, Y, Z and then the yaw angle.

And the power of Galois' mathematical language is it also allows us to create symmetrical objects in the unseen world, beyond the two dimensional, three dimensional, all the way through to the four or five or infinite dimensional space.

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

This includes the Cluster mission four satellites flying in formation around the Earth to provide a three dimensional map of the magnetosphere.

2D two dimensional

3D three dimensional

create scientific 2 dimensional graphs

It's all very one dimensional.

Stereochemistry is the study of three dimensional chemistry, as essentially understanding the actual three dimensional structure of things.

It s truly a three dimensional space.

This is a three dimensional machine.

So it becomes slightly three dimensional.

A two dimensional vector is needed

DCF Two dimensional Graphics File Format

Well, we take this three dimensional stack of images and treat it as a gigantic three dimensional coloring book.

Now, take into account the fact that we live in a three dimensional universe, OK, a three dimensional space.

The diamond structure is a three dimensional crystal while the graphite form consists of stacks of two dimensional sheets.

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

The charges of all known particles can be plotted in a four dimensional charge space, and projected down to two dimensions like this so we can see them.

Freeflying is more the three dimensional skydiving.

It s a thin film, two dimensional existence.

But their three dimensional orientation is still different.

So it's actually a multi dimensional user interface.

Or you could go into three dimensional art.

But the conflict was not simply one dimensional.

United Nations reform is all dimensional and multifaceted.

In fact, they live in a 12 dimensional space.

And she was talking about seven dimensional, inverted universes.

Clients are also demanding real time, multi dimensional information.

8. Vulnerability, then, is rarely a one dimensional condition.

One idea is that our three dimensional universe may be embedded in a high dimensional space, just as you can imagine on these sheets of paper.

Because a DNA sequence is a one dimensional entity, it lends itself much better to single number comparisons than a four dimensional body does. The genes that lead to the production of the human and chimpanzee femur may be 98 99 identical, but it is impossible to say whether the bones themselves are more or less similar than that.

This way you can make recursive and multi dimensional arrays.

And it randomly generates points within a three dimensional matrix.

Two and three dimensional mathematical modelling programmes have been devised.

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.

They can be planar formations, they can be three dimensional formations.

Middle board of this three dimensional chess game economic power among states.

Cars are three dimensional objects that have a fixed position and velocity.

Poverty is a multi dimensional phenomenon associated with economic and structural problems.

More intricate three dimensional assemblies have been produced through complex synthetic routes.

Dongyuanjinyue, which is in the immediate vicinity of Nanping Business District, has a better shopping environment. At its sole disposal is Western China s, and indeed, the nation s leading four story three dimensional transportation system, enhancing shopping comfort.

The musicians played off a three dimensional graph of weather data like this.