DR. JAMES GRIME: Have you ever heard of the time when they
tried to redefine pi, to redefine pi
so that it was 3.2?
BRADY HARAN: I'm about to.
DR. JAMES GRIME: Yes, you are.
This is absolutely insane.
It's a true story, as well.
And it's absolutely crazy.
So this happened--
well, I don't think that long ago.
It was 1897.
And there was a guy called Edwin Goodwin, this amateur
mathematician who thought he had solved one of the unsolved
problems of mathematics, a problem that goes way back to
ancient Greece.
It was called squaring the circle.
The problem is can you find a square that has the same area
as a circle.
So this problem goes way, way back.
And it's a favorite problem for amateur mathematicians.
And this guy thought he had solved the problem.
But implicitly in his proof, he had assumed that pi was
exactly 3.2.
Now, he was so pleased with his proof, he wanted to
copyright the proof itself so that anyone using the proof
from that point on would have to pay him royalties.
But he decided that the great state of Indiana--
which is where he was from-- that the educational
establishments of Indiana could use it for free.
How kind of him.
And so what he did was he had a bill made up.
And he tried to pass it into law that would recognize the
mathematical truth that he had discovered.
But it would allow Indiana to use it for free.
Though I think he had a friend, someone he knew, who
was part of the House of Representatives in Indiana.
And he made up this bill saying that the great
mathematical truth of squaring the circle.
Now, this bill went through committees.
It went through the Education Committee in the House of
Representatives.
And they obviously didn't know what they were doing, because
they passed the bill.
And the representatives actually passed it
unanimously, 67 to 0.
They passed it.
Now, this is the weird bit.
On the same day that they were passing the bill, there was a
mathematician in the building.
He was there for a completely different reason.
He was a guy called Professor Waldo.
But he decided to sit in on what they were discussing,
because it was about math.
So he was interested.
And he couldn't believe what he was hearing.
They invited him to meet Edwin Goodwin.
Oh, do you want to meet Edwin?
We're very proud of him.
He said, no, I meet enough crazy people as it is, thank
you very much.
So this mathematical professor then decided
to coach the Senate.
The next thing that happens is the bill goes from the House
of Representatives to the Senate.
So this professor coached the senators so that they knew
what they were doing.
By this time, the newspapers had heard of it.
They were mocking what was going on.
So when it reached the Senate, they threw it out.
They threw it out not before having a bit of fun with it.
They had about half an hour of maths puns and
making jokes about it.
Then they threw it out.
But seriously, there are solutions--
"solutions"--
to squaring the circle, where you take really good
approximations to pi.
More serious mathematicians--
for example, Ramanujan, who was an Indian mathematician,
and a brilliant one at that--
he had a solution to this as well.
So Ramanujan came up with an approximation which meant that
if you made a circle with an area of 140,000 square miles,
then you could have a square with the same area.
And the sides of the square would be off just by an inch.
So Edwin Goodwin had done this in 1897.
And you can see the documents.
It's absolutely true, this story.
You can look at the documents yourself.
You can read it.
And it's a strange thing to happen, as well.
Because the problem he was trying to solve, squaring the
circle, was proved to be impossible 15
years earlier, in 1882.
So I think we should have a video about squaring the
circle and what it means.
BRADY HARAN: Shall we do that?
DR. JAMES GRIME: Shall we do that?
BRADY HARAN: We'll film that.
We're about to film it now.
Tune in soon.
And we'll show you about squaring the circle.
DR. JAMES GRIME: Let's have a look at what you can do with
rules and compasses.
You can add numbers.
Look.
Here's a line.
And it has length a.
Then I add another line of length b.
And the whole thing is a plus b.