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.
