Venn diagrams, One Direction and Simon Pampena

What does Simon have to say about One Direction? Watch this and learn what a Venn diagram is!



Hi. My name's Simon Pampena and I'm the National Numeracy Ambassador, and I love maths. Why?

Well, because it's very useful at getting what you want.

Now what might you want? Well you might want to know how to model the universe with physics, you might want to know how to model environmental systems, you might want to know how the human body works with biology.

But let's face it, what you really want, well perhaps you want to be famous. Well you know what? Maths can help you become famous, and it doesn't even have to be very difficult maths, it can be just very simple maths. Let me show you what I mean.

Here is a very simple piece of maths. This is called a Venn diagram, and what's beautiful about a Venn diagram is that it's a way to analyse things that look separate but perhaps can be combined. So what happens with a Venn diagram is this circle represents something and this circle represents something, and somehow in the middle it's a combination of the two. Now how can you become famous with a Venn diagram?

Well what you can do is you can grab two things that people already like and somehow work out some way to bring them together. Let me give you an example.

People like fruit and people like cake, therefore fruitcake.

It's pretty nice. Big seller. Let me give you another example okay? People like puppies and people like side swept fringes, therefore One Direction, a big hit.

In case you don't know who One Direction is, here they are.

Now you should know their names, unless you've been living under a rock. That guy there, that's Niall. That's Liam, that's Harry, that's Zayn, and this guy Louis. What's great is these guys are an expression of the beautiful world of maths, this wonderful combination, but in actual fact we can use our Venn diagrams even further to understand how this band has been put together. Let me show you what I mean.

Because if we actually move them around and combine them, what we find is that these guys actually form a Venn diagram in themselves, and the middle the combination between Harry, Zayn, Louis, Liam and Niall in the middle is One Direction.

But you know what? Now that we've put this into a mathematical context, what happens - hopefully this doesn't happen - if we remove one of these circles, so if we remove Harry, what band would be left?

Well the band obviously would be a new direction for this band, but we could keep going.

If we took out Zayn, that would be a wrong direction.

If we took out Louis, that would be a misdirection, and if we just had Niall, well Niall, that's directionless, and of course we could have no band at all, which is no direction.

But no, let's actually bring it all back and let's not imagine that terrible fate of not having this band One Direction. But the question we've now got, is that that was just one way of combining or pulling apart, but we see in the Venn diagram that there's all different types of bands that could be possible with these members.

For instance there could be just a duo with Harry and Zayn, or may be a trio with Harry, Zayn and Louis, and that would sit right there.

So now by looking at this we could ask the question, how many sub-groups could we form out of One Direction?

Well let's count. A band with five members.

Well there's only one band, hence One Direction.

If we wanted to have a band with four members, well what we do is we'd have to take out one of them. That would be one band. Take out another one, that would be a second band, take out another one, that would be a third band, another one a fourth band, another one a fifth band. So there's five ways that we could have four band members from One Direction.

But what happens if instead we want three band members?

Well that's even trickier still. So if we take out 2, we get 1.

we take another 2 there, we get 2. Another 2 there, we get 3, 4, 5, 6, 7, 8, 9, 10 bands. So with this maths, so far we've actually got 10 + 5 + 1 different bands that we could make with these five members. The question is, how many bands could we have? How many different sub-groups could we have from just One Direction? How many directions could they

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