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Phi Challenge -

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Phi Challenge

Reporter: Paul Willis

Producer: Evan Wilkes

Researcher: Nicky Ruscoe


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20 July 2006

In nature exists one of the great mysteries of mathematics.

Phi, or 1.618, is a unique numerical ratio that can explain the proportions of the human body the
shape of a sea shell and the secrets of the beehive.

Or so Dan brown would have us believe.

If you've read the DaVinci Code you'll be familiar with Phi - the so-called 'golden ratio'.

But is it really all around us as the DaVinci code claims? We look at four famous examples of where
this number is meant to exist to see just how ubiquitous it really is.


Narration: I'm on a mission to find out the facts behind the figures, and my quest starts here, at
the University of Melbourne

I'm here to meet mathematician Marty Ross one of the country's foremost experts on Phi, which is
commonly known as 1.618

Marty explains that Phi is inextricably linked to that famous arithmetic progression the Fibonacci

Dr Paul Willis: That's the Fibonacci sequence isn't it?

Marty Ross: Yep

Dr Paul Willis: How's it determined?

Marty Ross: Well, you start with one and one, two is one plus one, three is two plus one and so on.

Dr Paul Willis: ok, so we've got the fib sequence, and I think I understand Phi, so what's the
relationship between the two?

if you take two fib numbers next to each other and divide them you will get very close to Phi.

Narration: A quick trawl on the internet reveals that Phi and the Fibonacci sequence seem to be
developing their own cult.

Within the mathematics itself, the equations for phi, the equations for Fibonacci numbers..(audio
jump cut), it's beautiful, it's beautiful mathematics.

Phi fanatics, or Fibonuts as they call themselves, claim there's hundreds of examples of both
appearing in the natural world. But is it just urban myth? Marty and I are going to put four of
these claims to the test. Keep watching and we'll reveal whether or not all the fuss about Phi and
the Fibonacci sequence adds up. My quest to find out the truth about Phi, the mysterious golden
ratio, and its curious cousin the Fibonacci sequence continues. Phi fanatics claim this number,
which has a value of 1.618, and the Fibonacci sequence can be found all around us in nature.

But I think it all seems too good to be true, so we're putting four well known examples of this
urban myth to the test.

In the da Vinci Code, Dan Brown claims these mathematical curiosities can be found in the nautilus
shell. It's found by measuring from the centre to the outer radius and dividing that by the
distance from the centre to the inner radius.

Marty Ross: Now if you divide those two we get 3.104

Dr Paul Willis: so that's nothing like Phi.

Marty Ross: No, and you can juggle it in all kinds of different ways but however you juggle it
you're not going to get Phi.

Narration: So, we've struck out first time at bat. Let's have a look at the most famous claim about
Phi appearing in nature is a person's height divided by the distance from the naval to the floor

Marty Ross: Ok, if we divide them we should get Phi but in fact we get 1.592

Dr Paul Willis: So even in a beautifully proportioned human being like karolina here we still don't
get phi?

Marty Ross: No, we get close but we still don't get Phi

and there's two versions of that, one version is that all bodies have that and the other is that
beautiful well proportioned bodies have this properties and both are false.

Narration: So, it's not looking good for Phi, let's try the insect world. According to Fibonuts the
ratio of female to male to male bees should be Phi, 1.618

But even Marty was flummoxed on this one, so we thought we'd get it straight from the bee keeper.

Graeme Grigston: We believe, depending on the time of year

it could be down to about 50 to one.

Dr Paul Willis: Not even close.

Narration: That's a third strike for Phi, but when we delve deeper into the ancestral patterns of
bees, we discover that the Fibonacci sequence, related to Phi, makes an appearance.

Marty Ross: Well, a female bee has both a female and a male parent, but a male bee has only a
female parent, so if you count up the number of parents and grandparents of each generation, you
get a fib number.

Dr Paul Willis: And that's going to occur for every bee in the hive?

Marty Ross: Every bee in the hive.

Narration: Our last example is the sunflower, allegedly the Fibonacci sequence can be found forming
a pattern in its head.

Dr Paul Willis: Marty, it's stunningly pretty, but where can you find (audio jump cut) fib numbers
in the head of a sunflower?

Marty: well the obvious thing your eye catches are these spirals going out like that, and if you
count the number of spirals going clockwise, that will be a Fibonacci number, and if you count the
spirals going counterclockwise, it will be an adjacent fib number.

Narration: For example, if a sunflower head had 21 spirals in one direction, it will have 34, the
next number in the Fibonacci sequence, spiralling in the opposite direction.

So, Phi is not found in the spirals of a nautilus shell nor the proportions of the human body, but
the Fibonacci sequence reveals itself in the ancestry of bees and the head of a sunflower.

But, that's still a strike rate of fifty, fifty, not bad for an urban myth really. So what's going
on here?

Marty Ross: If they exist in nature it has to be because somehow you are getting the next object as
the sum of the previous object, that's the way fib numbers work, two plus three equals five, five
plus three equals eight, when they exist in nature it's because that law, that rule is built onto
the natural mechanism, what ever it happens to be.

Narration: But why has the divine proportion been blown out of proportion?

Marty Ross: If you can get a great name, and people hang onto the name, if you have something like
the golden ratio, the golden mean, the golden proportion the divine proportion, these names suggest
beauty then you kind of except it as being beautiful whether or not it's really there.

Narration: So, there you have it, the golden ratio, fact or fallacy, well, it's a bit of both

Story Contacts

Marty Ross


University of Melbourne


Vic 3010