JAMES GRIME: We're at Numberphile HQ.
We're in Brady's house.
We're in Brady's garden, because today we're going to
take part in an experiment.
So this, what we're going to try and discover, are
Fibonacci numbers in nature.
Now, we have filmed a video about Fibonacci, but we
haven't edited it yet.
It hasn't gone up yet.
So this is a kind of precursor to that video.
Fibonacci numbers are famous numbers in
mathematics, though.
You probably know of them.
It starts with 1, and 1, and then you keep adding the
previous two.
So 1 plus 1 is 2.
Then you add the previous two numbers, so 1 plus 2 is 3.
Then you do that again.
2 plus 3 is 5.
Keep going, 3 plus 5 is 8, then you get 13,
and 21, and so on.
That's the Fibonacci sequence.
So you'll find Fibonacci numbers in nature.
If you pick a flower and you count the petals, it tends to
be a Fibonacci number.
That's why four-leafed clovers are so rare.
It's because 4 is not a Fibonacci number.
3 is but 4 isn't.
If you look in spirals of a pine cone, you'll find
Fibonacci numbers.
And what we're going to do is this summer, we're going to
try and grow some sunflowers.
And in the head of the sunflower, that's just packed
full of seeds.
And they'll grow in spirals.
And the number of spirals, again, tends to
be a Fibonacci number.
Imagine it like spokes of a bicycle.
But instead of just straight radially coming out from the
center, they'll curve, so they're spirals.
Like spokes on a bicycle, then, you can have more than
one spiral.
And we expect it to be maybe 55, that's a Fibonacci number.
Maybe 89 if you've got a large sunflower,
that's a Fibonacci number.
So we're doing this to celebrate Turing year.
So this year is 100 years since the
birth of Alan Turing.
Alan Turing is one of our great 20th century
mathematicians.
He was a mathematician, a World War II code breaker,
father of computer science, and was interested in
mathematics in nature.
This problem was one of the problems he studied near the
end of his life.
So to celebrate the life of Alan Turing and to brighten up
Brady's garden a little bit, we're going to plant some
sunflowers.
There haven't been many studies of this.
I mean, there have been studies before, but not many.
There was one in 1890.
There was one in 1930s.
And that's been about it.
So Manchester Science Festival have decided to create this
big experiment this summer for everyone to plant sunflowers.
We're encouraging you to do it as well, to join in.
And what we can do then later, in maybe September, is count
the spirals you get in your sunflowers.
Maybe take a photograph, send it in to the people at
Manchester Science Festival.
So I've got a selection here.
I've got dwarf sunflowers.
We've got here middling size sunflowers.
Awesome sunflowers--
massive, giant sunflowers.
So we've got Brady's sundial over here.
Brady likes it because it's got numbers on it.
Stick it in the hole, and our sunflower seeds, and hope
Brady doesn't mind.
Planting them in the sun, that's what we need, and this
is perfect--
right in the sun.
One down there.
There you go.
Now we wait.
Now we play the waiting game.
So we're going to plant the dwarf sunflowers in the pot.
So I think that will work.
So we're going to have to fill it with compost.
There you go.
MALE SPEAKER: What's the mathematical or natural
scientific advantage to having a Fibonacci number of spirals?
JAMES GRIME: Well, there is an advantage.
Because by having a Fibonacci number of spirals it allows
the seeds to be packed efficiently.
So if you packed them like it was spokes on a bicycle--
let's say it was every quarter turn, so you get four spikes
coming out from the center.
You've got all this dead space.
That'd be no good.
So you don't want to pack it like that.
Maybe you want a pack it every 12th.
You do a 12th turn, and then you put one in, and then you
do a 12th turn and put one in.
But again, you get lots of dead space.
So you don't want it to be a fraction of a full circle.
So you want it to be an irrational number.
So by doing that, it packs them in more tightly.
If the irrational number can be approximated, though, by a
fraction, you'll still get quite a lot of dead space.
What you want is an irrational number that can't be
approximated with a fraction--
or at least approximated really badly.
Now, there is an irrational number that is the most
irrational number.
By which I mean it can't be approximated by
fractions very well.
That is a number called the golden ratio.
It is the most irrational number.
The best you can do to approximate it is to use
Fibonacci numbers-- two Fibonacci numbers
dividing one another.
Two consecutive Fibonacci numbers
divided by one another.
So 55 divided by 89 would approximate the golden ratio.
And we will tell you more about the golden ratio in our
upcoming video.