ROGER: It's a magic square.
A magic square is an array of numbers which you put in
columns and rows.
So in this case, there are four rows and four columns,
going up and down, and you put a number in each.
And the idea is to make sure that the sum of all these
numbers going down in each column is the same.
And the sum of all numbers in each row is the same.
And the diagonals.
And the other diagonals.
So I want to draw in a particular way my favorite
magic square.
And there are bigger magic squares.
There are different famous magic squares, such as the one
in Durar's painting.
But this--
I want to draw, showing you how it has extra special magic
properties.
BRADY: Extra-special magic properties?
That's a big promise.
Are you going to be able to live up to that?
ROGER: Well, you be the judge of that.
So I'm going to draw a square.
Hopefully draw a square.
And put in four columns, four rows.
And I'm going to write the numbers in a particular way,
such as in a modern calculator.
So I'm going to write this as 2, like that.
And as 5--
oops, that's meant to be square.
And then 18.
And I'll do 18 as two boxes.
And then 51.
And 82.
This is going to take a time, Brady.
This is a magic square.
Let me show you why.
If I add up all these numbers in each row, they come to the
same total.
If I add up all these numbers, that row, that row, that row,
and that row, each one comes to the same number.
Or this diagonal, or that diagonal, they add up-- or
this little square in here, they all add up to the same
number, which is 176.
I'm writing it in normal curly numbers.
You'll see the reason why in a minute.
This 28, plus 15, plus 52, plus 81, is 176.
They're all the same number.
That's what makes a magic square.
If I do a diagonal, 58 plus 21, plus 15, plus
82 is equal to 176.
So this is quite remarkable, that somebody could dream up
something--
52 plus 15, plus 21, plus 88 is 176.
51 plus 15, plus 88, plus 22, is 176.
So whichever way you go, diagonal, across, down, check
it out for yourself, it adds up to 176.
Well, let me show you what's different about the way I've
drawn this.
If I now turn it upside down.
I have 11 plus 22, plus 58, plus 85,
which is equal to 176.
82 plus 51, plus 25, plus 18 is 176.
And you go through--
28 plus 15, plus 81, plus 52--
is that 52?
I can't write.
Yes, that's 52.
That's 176.
So whether you read it upside down or backwards,
it's still the same.
But there's even one more thing.
One more thing, which is absolutely beautiful.
I can now get a mirror and place it next to it.
And you will be able to see the top row
reads 28, 82, 55, 11.
And the next row is 15, 51, 88, and 22.
These also add up to 176.
So this is not only a magic square which I can turn upside
down, I can also look at it reversed in a mirror
and it's still 176.
So this is why this is more than just a magic square.
It is a magic square in different ways--
reversing, and mirror imaging.
And I find that incredible.
It wouldn't have existed, of course, before we had these
modern ways of writing twos and eights and fives.
Of course, you can't do it that way 'round.
That doesn't work.
That doesn't make any sense at all.
So it's only up and down.