The Alhambra somehow asks all of these questions.

Asymmetrical

Symmetric Point

Symmetrical its central body mass.

An object reflected in a point

The Rubik's Cube.

Steps toward unification exhibit the simplicity.

An object reflected in a line

Okay? So I want you to think about that problem as we go on, and count how many symmetries there are.

Reflect in Point

Reflect in Line

Symmetrical encryption

Only more debts.

so...

Reflect in this point

Constructed each plank of gold.

And this enables us to distinguish why the symmetries of these objects they both have six symmetries.

It's s over s squared over s squared plus a squared.

I don't always know why I take photographs of things.

Five symmetries and then of course the zeroth symmetry where I just pick it up and leave it where it is.

Reflect in this line

The earth is not symmetrical about the equator.

So if there's a 1 in this I J position, then there is also a 1 in the J I position, which in this picture seems like it'd be really nearby, which means that this matrix is symmetric, and I'm not going to get into matrix terminology but again if you're familiar with it, you'll recognize what a symmetric matrix is.

It's the reflection, so it jumps up here. then it goes like this and then it goes like this.

Select the line to reflect in...

And then in the second quadrant it looks like this.

It looks like oh let me try to draw this symmetric.

And the spider's web is for the reins on the horse.

This length is going to be the same, d1 is is going to be the same, as d2, because everything we're doing is symmetric.

Did you know that, in French, one doesn't hear the difference between the symmetry and the asymmetry ?

Reflect this object

Select the point to reflect in...

But it's not just scientists who are interested in symmetry.

And he said, Dan, what's wrong with you?

What is all that about?

and Bob Mills put forward, 50 years ago, this generalization of Maxwell's equations, with a new symmetry.

But on a larger scale of biology, actually symmetry is very important, because it actually communicates genetic information.

You have all of this business to the right of the y axis.

What crystals are possible, we can understand through the mathematics of symmetry.

So, Abell initally classified clusters simply on the basis of their appearance.

Galois has produced a language to say that in fact the symmetries underlying these are exactly the same.

Right there.

You see it already.

It's almost like little Sudoku tables.

So you might have something like this where you have a... maybe have a parabola, but it doesn't, it's not symmetric around the y axis and your temptation might be