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

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.

I would make a tetrahedron.

Now it matters what order you do the operations in.

create scientific 2 dimensional graphs

To illustrate why this is an interesting problem let me start with a quiz.

We can go from that cube to that cube.

Geometry

Shape

Snake

Now, for Galois, there was actually a sixth symmetry.

Geometric Trapezoid

Geometric Diamond

So now my plane let me see if I can do this.

And notice when we did surface area. We got our answer in terms of sq cm.

1990s were very successful in the geometric aspect of vision.

Open and closed figures

Geometric Four Point Star

Geometric Five Point Star

Geometric Heptagon

Geometric Pentagon

Geometric Hexagon

Geometric Six Point Star

Geometric Seven Point Star

Block Arrow Pentagon

Geometric Octagon

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

The Taj Mahal happens to be a very symmetric figure, and therefore, even in a single image, you get the equivalent of multiple views.

Sorting multi dimensional array

And, on the right is open five, ten and two.

The new area we added are these rows over here.

And this is what a triangular prism looks like it has a triangle on one two faces and they are kind of separated, they kind of have rectangles in between. the other kind of triangular three dimensional figures as you might see would be pyramids this is a rectangular pyramid, cuz it has a rectangular, or it has a square base, just like that you could also have a triangular pyramid where literally every side is a triangle. but this over here is a triangular prism.

But here's an interesting example. With, extra assumptions even one image suffices.

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.

I don't know, I just don't know how to plot all of these data, right cuz I need

This is a vector field.

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

Geometry Properties

Recognition we'll spend a lot of time on that. Recognition of objects, people, activities.

Let's say we have a point, a zero dimensional shape.

For the remainder of this unit,

Geometric Horizontal Parallelogram

Geometric Vertical Parallelogram

The geography and choreography.

We hate to start girls.