Select the point to reflect in...

So, in this case, it's the horizontal axis.

So one thing to realize is that these two focus points are symmetric around the origin.

Right there.

You know what it means.

There's no way that you could this is the exact center point the ellipse.

Asymmetrical

Symmetric Point

The Alhambra somehow asks all of these questions.

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

Select the line to reflect in...

Reflect in Point

Reflect in Line

Symmetrical encryption

Only more debts.

But if I had to choose one building in the world to be cast out on a desert island, to live the rest of my life, being an addict of symmetry, I would probably choose the Alhambra in Granada.

Symmetrical its central body mass.

Reflect this object

You take a sphere, in three dimensions, you rotate around the center of the sphere, and all those rotations leave the sphere alone.

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

Third Neutral

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

so...

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

Reflect in this point

An object reflected in a point

21 is the closest.

Reflect in this line

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.

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.

An object reflected in a line

Select the object to reflect...

And then in the second quadrant it looks like this.

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

So that's two.

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

Because it is hard to make symmetry.

I can't flip it because I've put a little twist on it, haven't I?

It's almost like little Sudoku tables.

You could think of an isosceles triangle, over here.

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

But let's go back down to symmetries that I got for these two objects.

And again you can see that the more luminous ellipticals seem to have shallower profiles.

It requires a laboratory to see it in three dimension, but in two dimensions I think you can see the beautiful symmetry and illumination of a normal mind at work.