Batman Equation - Numberphile

Uploaded by numberphile on 30.07.2012


So we're going to do something that looks really complicated,
something actually, if you talk about maths, you go, oh,
no that looks horrific.
And then we'll see how it turns out, all right?
We've done it.
That is probably the most horrific equation we've ever
done on Numberphile.
But what does it mean?
Well, let's try this out.
We're going to plot it, right?
We're going to draw a graph in my computer here.
And now, I'm going to draw the graph.
And it should be-- let me make that bigger for you-- it's the
equation Batman deserves, but not one he needs right now.
Again, that is the Batman curve.
It was famous when it went viral last year.
A high school teacher designed this curve, this equation, so
that it would draw the Batman logo.
And he made it quite cleverly out of different curves and
straight lines.
Can I show you how he did it?
So here we've got some things that you may be familiar with.
Straight lines are quite easy to draw.
What he did, though, is we don't want
a circle for Batman.
We want an ellipse.
Has a slightly different equation, so
it looks like that.
Now, he turned this into his Batman wings.
Obviously, we don't want the whole thing.
That's not what the curve looked like.
He actually just used these two ends.
He found a way to multiply his equation, and the effect was
it hides some of the curve.
What happens here in this bit that's missing, this becomes a
complex number, imaginary number, which means
you can't draw it.
And that's what he did.
He just carried on doing that.
He just used curves and straight lines.
And let me show you what they look like to make his Batman.
Now, he used six curves.
Let's have a look at them.
So he used the ellipse.
And, oh, this is quite clever.
This is the bottom of the Batman symbol.
And these straight lines and these ones are going to form
his ears, very pointy ones there.
And then, there you go, some more curves.
That finishes off the picture.
You put it all together, and that's what you get.
That's the Batman.
So he hid parts of it using imaginary numbers, yeah, using
square roots, which would turn some numbers that he doesn't
want to find into imaginary numbers.
It was a very clever way.
He used the same curves, but now you can see he's hidden
some parts of it.
You put those together, and you put them together by
So he put it together.
He multiplied these equations together.
What do you get?
The Batman curve.
It went viral last year, but I wanted to do it, because I'm
very much looking forward to the Dark Knight coming out,
Dark Knight Rises.