Zipporah Corser Anu

Kayb ngalpa ngitha mura, which in my language means, G'day everyone.

Sebastian Kelly-Toiava

Yaama, which in my language is a form of greetings, and I'm a proud Ngiyamppa man.

Zane Carr

Today, I would like to acknowledge the Darug people of this land on which we stand.

Zipporah Corser Anu

On which we stand.

Sebastian Kelly-Toiava

On which we stand.

Zipporah Corser Anu

May the stars shine bright wherever you are, and guide you all.

Sebastian Kelly-Toiava

I'd like to acknowledge the spirits, the ancestors, the flora and fauna,

Joshua Kalaw

the mountains, the rivers, and the Elders both past and present.

Zoe Brown

For they will continue on sharing their knowledge to the future generations.

Kiya Slockee

We pay our respects to your continued connection and care for Country.

Jared Smith

We would like to extend our acknowledgements to any other Aboriginal and Torres Strait Islander people here today.

Kiya Slockee

And so we welcome you to this beautiful Country.

Jared Smith

Sit back, duramori yurimaia, relax, and enjoy what I'm sure is to be an amazing gathering.

Yalabi daiyakung bora.

Yaama.

Eddie Woo

Hello everyone, my name is Eddie Woo, and it is my distinct pleasure to be with all of you today. Happy International Day of Mathematics, and I am coming to you from the lands of the Dharug people in Cherrybrook, New South Wales, Australia. I want to pay my respects to Elders past, present, and emerging, and extend that respect to all of our First Nations people who I'm delighted are able to join with us for today's webinar.

Our theme for today is Mathematics, Art, and Creativity, and I know when I hear those three words together, there's a small part of me that feels like maybe they don't belong in the same sentence, and part of what we're going to be having a look at over the next 45 minutes is how, in fact, these are not things which should be separated, but rather they are uniquely and wonderfully bound.

And in fact, this first image here is one of my favourite examples. It's a piece of art from a mathematician and artist named Clarissa Grandi, and just by looking at it, I wonder what you are thinking, what you are wondering about how mathematical this is, how artistic and how creative it is. I think it's certainly beautiful.

One of the things I think is most wonderful about mathematics, art and creativity is that they have been joined and united together for centuries, and I don't need to just, you don't need to just believe me for it. Let me give you some evidence.

These for example, are tiling patterns that you can find across the Middle East, often in mosques, and one of the reasons why is because Islamic Art, does not have any images of animals or human beings and so they turn to this source of eternal and universal beauty, mathematics and geometry, and you can see the wonderful symmetric patterns, the tessellations, the different polygons and how they all fit together which sort of demonstrate how bound together mathematics and art can be.

Now, I said this was an ancient example. We've been seeing these around the world and finding them for hundreds of years. But if we cast our mind into more recent times, you can see things which are clearly inspired by the past, but are also informed by what we're doing on the cutting edge of mathematics today.

What you're having a look at here is a piece of art that is informed by the golden spiral. Maybe some of you have heard of the golden ratio before. It's a piece of mathematics that we find all around us in the world, even if you have a look at your own hand and you look at the different relationships of the bone lengths in your fingers.

This ratio, the golden ratio, is even found within your own anatomy, but it's not just your anatomy. This particular spiral here, which is a piece of art, actually is further inspired by nature.

When we think about creativity, creativity is often, mathematical or otherwise, about connecting things together that are a bit surprising, that we wouldn't necessarily think make sense together. And so when we look out into nature, we can see patterns. This is a nautilus shell and it's spiral, which you can see those chambers track how the nautilus is getting bigger and bigger and needs to make itself a bigger shell, create something that is immensely beautiful and undeniably mathematical.

Now, I want to bring things a little bit closer to home, even though I know we have people tuning in from all around the world, and thank you, especially if it's a very interesting time zone for you. I want to take you to somewhere which has sentimental value to me, which is the National Gallery of Australia in Canberra.

This is one of my favourite artworks that's there. It's called, very appropriately, Cones and it's by an artist named Bert Flugelman. When Flugelman was creating this, he anchored the structure in a very bare environment and the trees that you can see around it were just little saplings. But as they grew up, I want you to look closely at this artwork, look at the reflections, look at nature demonstrated in these very artificial objects, which nonetheless, get to show that environment around us and we get to enjoy.

This artwork is really incredible. It's, it's took a lot of creativity and engineering to conceive of, let alone to make, and for me, I think that it's a fantastic illustration of seeing something in the built world. But something that is not in the built world at all, something a little digital in nature, is going to make your eyes a bit confused. At least it made my eyes confused when I first saw it.

This here that I'm showing you is an artwork by Kevin Walker. I know when I looked at it I thought, is this a maze? And it does look a little bit like something that I would take a pencil to and I would start drawing around and try to find my way from the beginning to the end.

It is kind of like a maze, but actually what this is technically called in mathematical terms is a spanning tree, or often a space filling curve. I know it doesn't look particularly curvy, but there is a mathematical equation that Kevin Walker the artist used to be able to fill up the spaces in this artwork so that there were no gaps and that everything wound around and was connected one to the other.

Space filling curves sound like something out of science fiction, but actually, coming back to your own body again, you are filled with space filling curves. Every blood vessel in your body, from the very largest ones to the teeny tiny ones that you can't even see with the naked eye, those little capillaries, they deliver blood, nutrients, oxygen to every cell in your body using a space filling curve just like this. And this is one of those ways that mathematics and art, which you're looking at right now, are creative, but also something that you find all around the world.

Now let's have a look at something that is completely artificial, but nonetheless, I think just really cool and incredibly artistic. I had the joy of heading to the United States for a little bit of a work trip at the end of last year, and one of my first stops was a place called the Museum of Mathematics in New York City, and in it, this is one of the art fixtures.

Now, it's a little bit confusing, I'll admit. Takes a bit of a moment for your eyes to know what's going on. This is a gigantic polyhedral chamber that is filled with mirrors all the way on the inside, and there are two holes that are cut out for people like me, as you can see in this image to stick their head through and be amazed at the different kinds of views and reflections of what's going on.

There are a few rainbow coloured lights in there, but not as many as you would think. We can just see lots and lots of copies of those lights. reflected back and forth off of all of the mirrored surfaces.

Now the Museum of Mathematics in New York City isn't the only place I got to visit while I was in the U.S. I went to a famous museum called the Guggenheim. Now the Guggenheim, the building itself, if you have a look at that left hand image, looking up into the ceiling has this beautiful spiral design to it, and as you go and see the artworks, you wind your way round and round and round. And for me, as I looked at that building and then got to admire some of the artwork in it.

And if you can have a look at this one on the right hand side, which was divided up into 64 sections, and this was by David Bomberg. It's called In the Hold. It's a more than a hundred year old artwork, and it's called In the Hold because if you look at it, and depending on your interpretation, what this represents is actually a ship, and the view from it, which is very geometric and full of different transformations.

So, these are some of the kinds of artworks that you see, which are deeply mathematical all around the world. But I want to bring things back into the more local area for those of you who are tuning in from Australia.

One of the most iconic buildings in the entire world is the Sydney Opera House. And I am extremely privileged to be able to live relatively close to the Sydney Opera House. It's just a train ride or a bus ride away.

One of the things you might not know about the Sydney Opera House, even if you recognise its shape and its profile, is you may not realise how intensely mathematical the building is.

Jorn Utzon, the architect, was trying to work out a way to manufacture these iconic sails, which are meant to look a little bit like that artwork we just saw, like a ship and also like a shell, and so there are all of these maritime metaphors coming together. But he was having difficulty coming up with an engineering solution for the Sydney Opera House until he stumbled on something that I'm about to show you in the video that's about to play.

Utzon's key insight was that you could take the uniform curvature of a sphere and nonetheless cut out many different shapes from it. Just like a single musical instrument can play many different songs, so too can a single sphere make many different shells. And this is how the iconic sails were ultimately created.

Now for me, when I have a look at this, I am amazed by the fact that you can take this simple shape and cut out different sections to make the iconic design, and I know it went very quickly on the video. So I will quickly show you a plaque that is actually sitting out the front of the Sydney Opera House.

So for anyone who gets the privilege of getting to visit it one day, have a look out on the grand stairs right at the front and you will see this plaque there, which illustrates just how all the pieces fit together. I'd love to read from Jorn Utzon's quote, which is just up there in the top left. I know the text is very small, but his quote captures again, the cohesion, the connection between mathematics and creativity.

Utzon said after three years of intensive search for a basic geometry, he's talking about the kinds of shapes he was looking at for the shell complex, I arrived in October 1961 at the spherical solution shown here.

I call this my key to the shells because it solves all the problems of construction. And he goes into some of the detail on that and he says, in conclusion, I attain full harmony between all the shapes in this fantastic complex.

And when I just behold this, I just admire that he was able to take a mathematical structure and make it so incredibly unique and beautiful, even though we've seen spheres all the time.

Now Utzon was not the only person to be inspired by the sphere. I want to show you some more recent artworks, very recent actually. This one on the left hand side is actually a 3D printed lamp by an artist named Bathsheba Grossman. So you can actually buy these online and you can plug them in and turn on the light, so long as you plug in the bulb properly, and you can see there are these starfish designs around the edges of the spherical piece of art that are all, one to the other, identical.

And so even though they are all differently arranged, they fit together in this one unique thing. And we couldn't have created this without the 3D printing technology that we have today.

The image that you see on the right hand side does also kind of look spherical, even though it was actually drawn as a flat piece of art by its artist, M.C. Escher. Some of you tuning in, particularly the teachers in the room, might have heard of Escher before. He was a Dutch graphic artist from the 20th century, and his artworks are intensely inspired by mathematics. And as we get toward the finish of this part of our webinar today, I want to show you one of my favourite artworks from him.

These three spheres are one of Escher's self portraits. You can see the sphere on the left is made out of glass, the sphere in the middle is made of silver, and the sphere on the right hand side is made of stone. That one in the middle is the one I want you to focus on. And if you look closely, you will see there's Escher drawing this artwork.

And because the ball is silver, we don't just see Escher in the artwork, we also see the piece of paper that Escher is drawing on. So there's a picture of the artwork. In the artwork, don't think about it too hard, it is quite confusing. But have a look at the piece of paper as we see it reflected in that sphere.

The piece of paper doesn't look like a nice neat rectangle, even though it is a normal rectangular sheet. The reason why is because it is distorted by the sphere, and Escher in his artwork represented this mathematical reality, which actually has real implications for us today. Let me illustrate.

Here is a map of the world. I love it because it shows, using satellite photography, what the different parts of the world, like the deserts and the forests and the mountains and the ice, look like. The only problem with this map of the world is that it is not a map of the world.

This is a real map of the world. The real world is spherical. And if we were to take the surface of this globe, cut it out with a pair of scissors, and then lay it out on a table, we would not get the map that you just saw. We would get something like this.

Have a think about why this is the shape that we would get. All of those lines that are running up and down, we call them meridians of longitude, they all meet at the North Pole and at the South Pole.

In other words, those lines converge. And so when we cut this map out from the globe, those parts will become sharp and pointy, leaving us with these gaps in between. Now, even though this is an accurate map of the world, it's not very useful for navigating, especially if you're a sailor trying to make your way from one place to the other.

You'd just fall off the world here. And so in order to create this map, cartographers, which is the name of the people who create maps, and mathematicians worked together to fill in all of those gaps. by stretching out the parts of the map that you saw before into all of those white spaces. But there's a problem, and you can see that problem if you look down the bottom of the map at Antarctica.

Antarctica is a big lot of ice, but it's not that big. Last I checked, Antarctica is not the size of every other continent around the world combined. And that's because of that distortion that was introduced to the same kind of distortion that you saw on Escher's artwork. I want to show you now, this is an animation, I hope that it's going to play for you, but I have a backup in a second.

I'm going to show you how each of the countries in the world have been distorted in size because of this projection.

I'll give you a moment to take it in. You can see that, some of the countries are stretched out a lot, like Antarctica mentioned down below, whereas some of them barely change in size at all.

Let me now hold it still for you and you can see which of the countries get a whole lot bigger than the dark part is how much they actually are. And the reason why there are differences is because when we were talking about stretching out the map, only some parts of the map are stretched.

Along the equator, the map doesn't need to be stretched at all, and so those countries are an accurate size. But in fact, everything else, things very far north or things very far south, they have to be stretched out a lot, and that's why their size is so exaggerated.

It's not just size by the way, here is the GPS tracking across a map of a swimmer crossing this channel and she was not swimming in a funny curvy line, she was swimming straight. But our maps distort her path and that's why you can see there is this funny looking curve that looks like she was taking the scenic route while she was doing her swim.

Once you realise this and see that there are so many different ways to mathematically look at the world, it really changes our understanding and each of these maps is its own creative solution to use mathematics to help us picture the world around us.

So, we've come to that really exciting time for me, where all of you get to use a bit of mathematics and art and creativity. So I know a lot of you have a handout that looks a little bit like this. If you don't have a handout, in the chat you might've registered a little bit later, we're going to be posting a link that allows you to explore this activity. But for those of you who do have the paper ready for you, as it's distributed around the room, let me explain to you how this is going to work.

There are instructions written on the page and you will get to choose a number, I think I've offered 2, 3, and 4, that we're going to do some multiplying and some drawing with. Let me kind of illustrate.

Every number that we have from 1 to 60, we're going to start with that. We're going to multiply it by a number and then draw something using that multiplication. So say for example, I chose the number 4. I'm multiplying by 4 all the way through. So if I start with 1, 1x4 will be 4, and what I want to do is link the dots that represent 1 and 4 to each other.

So you can see if you've got a ruler there that will really help because it'll make your drawing nice and neat and will emphasise the effect that we're going to get.

That's just the first number and the first line after that I'm going to look at the next number, 2, and I'm going to multiply that by 4 as well. Whichever number you choose, whether it's 2 or 3 or 4, make sure you stick with it as you go around the circle.

Now I've gotten 2x4 is 8, so 2 and 8 are the numbers that I'm going to join on the circle. You can see my red line there. I'm going to keep on doing this. 3x4 is 12, and you can see I've drawn a new line, and I'm going to do that all the way around the circle, but you have to be careful as your numbers get bigger.

For example, 14x4 is 56. I know I'm doing some of the work for you, but that's okay. It's just for the sake of illustration. So you can see in purple, I've joined the 14 and the 56 together. 15x4 is 60, so I've joined 15 and 60. But now I'm up to 16, and 16x4 is 64, which I don't have on my circle. You can see I only have the numbers 1 to 60 on my circle.

So if you get a number that's bigger than 60, what I would like you to do is subtract 60 from that number until you get something less than 60. So in this case, 64-60 would just be 4. So 16 and 4, those are going to be the numbers that I joined together because they are on my circle.

You might get a number that's even bigger. You might get 124. And in that case, what you want to do is keep on subtracting 60 until you get something less than 60. So 124 turns into 64. 64 would turn into 4.

You're going to have a lot of numbers and a lot of lines, but that's why I'm about to give you some time, roughly ten minutes to explore this. So, I hope you got your skates on and your pencils ready, the paper handed out.

I'm going to leave these instructions up on the screen for a few minutes, and then we'll be back soon to explore the next part, and I'm gonna, I'm really looking forward to your questions as well. So in a few minutes, we'll come back together.

But for now, good luck, and I'll see you soon.

Ben

Hi, Eddie. We have a question from Charlie. The question is, what is your favourite mathematical art piece?

Eddie Woo

Thanks so much, Charlie, for that question. I have a lot of difficulty in some ways answering this because I have a lot of favourite art pieces, but if I had to pick one, it's actually not one that many people might necessarily classify as an art piece but it's actually something that you can look up yourself and I encourage you to do this It's something called a fractal, but it's a particular fractal.

There are so many, there's an infinite number out there. It's a particular kind of shape. The particular fractal that is my favourite, and I'll tell you why in a second because it has sentimental value to me, is something called the Mandelbrot set. Mandelbrot is spelled M A N D E L B R O T. It was named after Benoit Mandelbrot, who was the mathematician who came up with this idea of fractals.

If you go and search for it, I'm gonna try and describe it to you, but words are gonna fail, and you really need to look at an image of it yourself. The Mandelbrot set is this stunningly, infinitely detailed two dimensional image that is made up of the relationships between different kinds of numbers, particularly a kind of number that you might discover about in a few years called, sorry, that was my timer for five minutes, called complex numbers.

The Mandelbrot set has a sentimental place for me because it was the first time that I saw mathematics as artistic. My brother, who's eight years older than me, showed it to me when I was just in primary school, actually.

And I looked at it and I said, what is that piece of art? It looks so strange. And he said, Oh, it's mathematics. And I had no idea that those two things could be combined together and it set me on this path of curiosity.

So Charlie, I hope that answers your question. Now since I have everyone's attention at the moment, what I'm going to do is start a new timer to give you a heads up. We've got about five minutes left before we move into the final section.

I'm going to start that timer. Now, if I can click on it properly, there we go. And while that timer is going, some of you may feel like I'd like to try something different or maybe you're exceptionally hardworking and you've already finished that task on that handout. In which case I invite you to have a look at this image here, which has four different objects on it.

And I would love you to answer the question, maybe in groups or with your class or with your teacher or whoever you happen to be with. Which one of these objects doesn't belong? Which one of them stands out? Kind of, maybe doesn't fit in with the pattern that you can see. And as you think about which one doesn't belong, the two follow up questions that are,

Why doesn't it belong? I don't just want to say, oh, it's that one. I want to understand your reasoning and your thinking and I also would love to suggest that potentially there isn't just one correct answer to this.

I know in mathematics often there is right and there is wrong, and that's one of the great things about you can you can get something correct and it's very satisfying but in many areas of mathematics questions are open. There are multiple solutions and sometimes comparing those different solutions one to the other is really, really valuable.

And so maybe there's more than one answer to this and it's not just the first thing that you think of. So just a few more minutes. I'm going to duck off for another moment and then we're going to come back together to close off this section and then head into the Q and A.

So just a few, few more minutes to go.

Meagan:

Eddie, we have another fantastic question that's come through the Q&A for you. People are wondering if we can use numbers other than 2, 3 and 4, and what if we subtract some numbers other than 60?

Eddie Woo:

Oh wow, that's brilliant, such a thoughtful question, and by the way, this is one of the best things about mathematics you're experiencing right now.

I have crafted this particular activity to go in a certain direction and to show you a particular idea. However, Mathematics is something which we can explore and ask questions of, and there are no rules around that. You can be the master of your own destiny in that way. Now what I will say is that, for the particular handout that I've given you, 2, 3, and 4 give particularly unusual and interesting results, which I'm going to explore in a second. That's why I've chosen them.

You can choose any number that you like, but I will say that the other numbers that you choose, the patterns that you get are more interesting and easier to see if you have more than 60 dots around the circle. If you have a 100 or 200 dots. Now because of the confines of time of this little session that we've got together, I didn't really want anyone doing that many calculations. I didn't think you'd have enough time to go all the way around the circle.

But one of the links that I think is going to be posted in the chat is to a little piece of technology, a little app that you can access via the web or even on your phone, that will draw all of those thoughts for you. I just wanted you to explore it on your own for now, but 2, 3, and 4, those are just my suggestions for today. Please explore this in your own time.

There's a good chance that you are still working away on those, and I'm really sorry that I'm about to spoil a little bit of what you're heading towards, but I hope that it's not actually a spoiler, but a motivator for you to complete this task and to explore other things.

I'm about to show you one I prepared earlier, because this is a fantastic task, I've explored it many times before. When you multiply 2, or 3, or 4 as your number, you get different kinds of shapes, and this is kind of what they look like, and maybe if you have a look at the number you chose, you might recognise the shapes that you're seeing here as forming just at the beginning, or maybe you're halfway around.

These shapes here are called epicycloids. Funny sounding name, and one of the great things about them is, you know, I've given you 60 dots around the circle, if you have more dots, I mentioned 100 before, you can see those epicycloid shapes even more clearly. Now, we've created them using multiplication and joining lines together with a process called modular arithmetic.

But these are not the first places that actually human beings discovered epicycloids. This kind of mathematical art was actually encountered when people were using wheels and turning them one against the other, like say when you've got gears that have interlocking teeth. You can see that this epicycloid on the left is the same shape that we created when we were multiplying by two and then going all the way around.

This shape that you can see here is what happens when you multiply by 3, and this last epicycloid over here is what happens when you multiply by 4. And when I saw these for the first time, I know my question to myself was, is this mathematics or is this art? And the conclusion I came up to after exploring many of the things that you saw today, is it mathematics or is it art? And the answer is yes.

Because mathematics is artistic and creative and so many parts of art and creativity are mathematical. So I hope you found these really interesting ideas to explore today. I've gone way over time for that section, so I apologise, but I am so looking forward to the questions that many of you have posed already and I think we even had a few that were sent in beforehand that we're going to see. So I'm looking forward to hearing those so I can answer them.

Leilani

Hi, my name is Leilani. I go to Lake Illawarra South Public School. Eddie, my question is, is there a biggest number or can you always add one more?

Eddie Woo

What a lovely question.

Thank you so much for asking that. Is there a biggest number or can we always add one and keep on making it bigger and bigger? Well, one of the things about mathematics, which I mentioned before, is that it's this imagined world. You know, if I'm adding on my fingers, I can go for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and then I can't say, well, add another one because I run out of fingers.

I suppose I could start going to my toes, right? But in mathematics, we can just imagine any number that we like, whether or not it exists in the real world. Now, obviously 11 exists in the real world, but some of the numbers that get bigger and bigger and bigger, say for example, you might've heard of a Googol, not G O O G L E.

I'm talking about G O O G O L, which is a number that Google, the company, was named after. That's a 1 with a 100 zeros after the 1. So it's an enormous number that it's not like we've ever counted it or found it necessarily anywhere in the real world. But nonetheless, we can imagine it. So therefore, I guess the answer to that question is No, there's no biggest number, which is kind of wild.

We can always make things bigger, and you can do it a lot faster than just adding one. There's all kinds of crazy numbers that you can see. I see that Googleplex has come up in the chat, it is very large. I don't think it is the biggest because we could always add one. If you're curious, you could look up Graham's Number, which is just mind bogglingly large.

But the large things that we try and explore, we can imagine them. That's one of the great things about mathematics.

Hannah

Hi, my name is Hannah. I am from Lake Illawarra South Public School. Eddie, my question is, if infinity goes on forever, can we have half of infinity? And will it still be infinity?

Eddie Woo

I love this question so much because it gets something, it gets at something really, really deep.

If you divide infinity by half, does it still go on forever? Is it still infinity? Now I've got two ways to answer that. Firstly, I want to say I understand the instinct around why if we have infinity, is it still infinity? Because ordinarily when we have things, they do tend to get smaller. So does that apply to infinity?

Well, the first thing I want to say is it already doesn't apply to some of the numbers that you know, for example 0. When you halve 0, it doesn't get smaller or bigger for that matter It just stays 0 and infinity is a little bit like that. So that gets to my second point, how do I really think about how can you halve it and it doesn't get any smaller?

Well, if you took infinity and you doubled it It's still infinity, right? So you've got infinity and double infinity and I think it's pretty uncontroversial that both of those go on forever. But now you've got an infinity that apparently is twice as big as the other one. So I could start from double infinity, halve that, and then end up with the infinity that I began with in the first place, which we already established definitely goes on forever.

And so, in fact, you can halve, or you can double, or quadruple, or you could quarter, any proportion of infinity is still infinity because we didn't build it through multiplication or addition. It is a concept that simply goes on forever, by definition. So, half of infinity, it goes on forever just as much as infinity does.

Will

Hi, I'm Will. I go to Lake Illawarra South Public School. Eddie, my question is, if we have a number that goes on forever, like Pi, how can we ever know what it really is?

Eddie Woo

Thank you so much for asking this question, and I have seen Pi appear a few times in the Q&A already, which makes sense. The reason why the, by the way, why the International Day of Mathematics is today, the 14th of March, is because in some parts of the world, the 14th of March is written as 3, the third month,

1, 4, which are the first three digits of Pi, but as the question points out, the digits don't stop at 3, 1, 4, they go 3, 1, 4, 1, 5, 9, 2, 6, and they just keep on going. They keep on going forever. So how can we know what it really is? Well, I guess in some sense, you can say, no, we don't know what it really is because there is an infinite number of digits.

They never repeat. That's what's called a recurring decimal, and so even though there is a pattern to be able to understand so we can keep on calculating the next numbers, and we've got a lot of formulas to do that and big powerful computers that have millions and millions of digits of Pi, we're never going to get all of them.

However, I would say that even though we don't have all the digits of Pi, we can still know what Pi is. So let me try and illustrate this for you, right? I am beaming to you from Cherrybrook Technology High School, which is the school I've taught at for the last many years now, and I can tell you what the address of Cherrybrook Technology High School is.

It's 28 to 44 Purchase Road, Cherrybrook, New South Wales. Now that street address doesn't tell you down to an exact, you know, position where I am. Like it doesn't give you latitude and longitude and coordinates and things like that, but it does tell you enough to work out where my location is. You could come to me, you could say hello.

And when it comes to Pi, we can have enough digits that anything we needed to do, we could be accurate enough. In fact, even though I mentioned that we've had calculators and computers working out millions of digits of Pi, famously, you only need about. The first 100 digits to be able to calculate things like the width of the known observable universe to an accuracy within the width of a single proton.

So even though we can get never ending precision, we don't necessarily need it. In the real world, often all we need is accurate enough and that will do, that will solve all the problems that we actually need.

Meagan

We have a few questions from the Q&A for you, Eddie. Patrick's class has a really deep philosophical question for you.

They want you to answer, what is maths to you?

Eddie Woo

That is a really deep question, and hello Patrick, been a little while since we've caught up. I'm so glad you got to bring your class along. What is mathematics to me? I definitely don't have a single answer to this question, and I guess that's what happens when you spend, you know, it's been almost 20 years of my life now that mathematics has been a part of my job.

So I have a lot of answers to this. I guess the first thing that I would say is that mathematics is the language of the universe. It's what helps us understand all the different things around us. You saw so many examples that I gave today of how nature Is expressed and understandable through the laws of mathematics.

And in fact, there was a physicist in the 20th century named Eugene Wigner, and here we're at a paper where basically he said we don't know why mathematics is so awesome at explaining and helping us comprehend the world around us, it does, we should just be grateful for it. So number 1, it's the language of the universe.

But number 2, and maybe I'll just give two answers because I know there are other questions as well and I'm watching the clock. Number 2, for me, mathematics is something really personal. Mathematics enables me and all of us to be able to not just appreciate the natural world, but also to navigate my own life.

It allows me to make sure that I can buy enough food to feed my family, to be able to have a job and manage my money. It helps me in my garden when I'm trying to measure out a garden bed and plant different seeds and do that in a way so that they'll grow and they'll thrive. Mathematics helps me. to flourish in the world.

It helps me to solve problems that I've never encountered before, that I don't have a formula or an algorithm to help me solve. It helps me to persevere when I'm trying to understand a situation that is confusing to begin with, but mathematics has equipped me with a toolbox and a disposition to say, I don't know what the answer is, but I can work it out together with the people that matter to me.

And I guess that's the reason why I love teaching this subject. It's a subject that empowers us and gives us the ability to navigate the world around us and live in a way that is positive and enjoyable and enriches my understanding experience of life. So those are a couple of things that mathematics are to me.

Now, like I said, I am looking at the clock. I reckon I'm going to fit in two final questions if I can talk fast enough. So let's see what the last two are.

Meagan

Okay, so Joe from Toormina High School would like to know can you think of any foods which contain interesting mathematical patterns?

Eddie Woo

Oh, yes, absolutely.

And hello, Mr. Anderson and everyone at Toormina High, great to have you tune in. My favorite piece of, my favorite vegetable, which has a piece of mathematics in it. Oh, no, I've got two now. Okay, I'll give you both. The first one is this very specific kind of broccoli, and I apologise, I don't have the name off the top of my head.

But I promise if you go to Google and if you search fractal broccoli, you will find it. This kind of broccoli, as I just mentioned, it's a fractal. This is the same kind of shape I was mentioning before. Every little part of the broccoli, if you cut it off and look at it, it's like a miniature copy of the whole head of broccoli.

And you can do this down and down and down from a large, a full head down to like little millimeters. Every different version is what we call self similar. The other example I was thinking of was actually a capsicum, and that sounds really weird, but if you cut a capsicum and look at it inside, you can see there is this shape to it.

There are usually, you know, these sections to it that actually look a whole lot like the epicycloids that we were drawing today. So I think you've got to cut it across and then hold the stem and look at it, look at it from the top or the bottom, depending on your perspective.

So there you go. I'm sure I could think of a few more examples if I had more time. Shall we have a listen to one final question?

Meagan

One more quick one. Jodie would like to know what is your favourite number and why is it 37?

Eddie Woo

Oh, Jodie, that's, that's sneaky. Well, Big Bang references aside, Big Bang Theory references aside, my favourite number is, I, my favourite number is a bit like my favourite song, which is to say that as time passes, I just have different ones, which maybe makes me sound like I just can't make up my mind, which is probably true, honestly.

I think I would have to say, this sounds strange, but my favourite number is 1, because every other number is made up of different copies of one or ways to divide it up, and 1 is the ultimate building block. All the rest of the numbers that we find all around us, which have given us the things to explore today.

So we said that was the last question. We are right on time. What I'm going to say is thank you so much for joining us. I've had a great time. I hope you've enjoyed this as well and seen a few different ideas and concepts, and as you go out from here, you will see the connections between mathematics, art, and creativity.

As a final pointer, I'm sorry to all the people whose questions I didn't get to but I'm going to do my best to go troll through the Q&A afterwards and with any luck I'll be able to maybe put together a video and send that out across to everyone who has registered. So, your questions are not going to waste.

Thanks everyone again for coming today. Have a fantastic rest of the International Day of Mathematics and I hope I get to cross paths with you soon. Bye!

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Duration: 5 minutes 22 seconds

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Eddie Woo

The thing I love most about STEM is that it flips upside down the learning paradigm for students, especially in something like mathematics. We often have students answering questions that have been posed to them by the teacher or the textbook. However, STEM reverses that and actually has students themselves generating questions that mean something to them because they've got a problem that they want to solve.

And so they themselves are the ones coming to me saying, Sir, we're trying to solve this problem. How do we do it? And I'll say, I know exactly a tool for it, and then I can introduce the maths. One of the things that's most profound and powerful about mathematics is the universality and the timelessness of the things that we know and we can prove in maths.

For example, Pythagoras Theorem is all about the relationships between the sides of a right angle triangle. Now, Pythagoras theorem was true thousands of years ago and it will be true thousands of years from now, long after any human beings are around to know about it. And that's because it's about something deep and timeless and it's not dependent on culture or our context.

It's something which we can say to anyone around the world and they can say, Yeah, I agree with that. And I think in our world today, those kinds of things are in short supply. So it's a wonderful, unifying theme to be able to experience and see mathematical truths together and to actually agree upon them. In terms of making mathematics meaningful and connecting it to the lives of our students.

I think one of the most important things to recognize is that mathematics looks on the surface like it's about symbols and algebra and things like that, formulas that maybe a student might say, When am I ever going to use this in everyday life? But actually, mathematics is really about helping students think in a deductive and a formal and a logical way.

And it doesn't matter what problem you're encountering. Actually, all those things that we look at in algebra and geometry and trigonometry, they're just examples that give students kind of a practical context to say, how can you create something that really proves to me in a watertight way, in a convincing way? I'm persuaded that this has to be true.

A lot of the ideas that we encounter, a lot the skills that I want to teach students in mathematics, they take a lot of effort and work and they overload your working memory, they’re hard work. I don't shy away from that. One of the things that's really important there obviously, therefore, is student motivation. A student's going to care enough about wanting to solve this problem that they'll put in the time and the effort to develop those skills.

And I think when we give students a situation where there's a genuine problem they have to solve patch, it's local to their community. It's something they encounter every single day. And we can say, you know what? There's maths, there’s scientific knowledge. There is technology solutions that can help us do something about this problem that means something to you, that matters to you.

And often that's the key. Having it connects them in a personal way that I really love because maths can be so abstract. Sometimes it can feel like solving a bunch of problems that I don't care about, so why would I bother and put the effort in? So giving them a reason to care I think is really essential. There's these core skills that run across all of the different parts of maths that are meaningful to you, whoever you are and what have you interested in doing in life.

Now we must call these working mathematically. They are the skills, they're the qualities that we employ every time we solve a math problem. The things like communicating, understanding, problem solving, reasoning and fluency, these are things that matter every single day. Whether you're going to go into something super mathematical in your career, like, say, engineering or finance. But they're also there.

If you're an artist, if you're trying to write a compelling legal argument, there are points where those mathematical principles and skills are meaningful to you, whatever sphere of life that you're in. So I think focusing on those working mathematically outcomes are really the best way to help a wide variety of students connect to mathematics. As educators and people who work with young people, we really have a responsibility and the privilege of helping our students see all the wonderful contexts and practical applications for mathematics.

And it's really important that we show our students this so that they recognize that they're not just doing maths because we tell them because it's homework, because they have a test. But actually it helps us solve problems that really matter and it enriches our understanding of the world. I'll give you an example. Calculus isn't just about following a bunch of rules and formulas to get some answers out of manipulating symbols.

It's actually about the mathematics of change, whether that's temperature that fluctuates or population that goes up and down, or the position of the moon in the sky. All these things can be understood and articulated using calculus. So if we can show our students a context that means something to them, whether it's about trying to fight a global pandemic or trying to work out what's the way to minimize the amount of plastic waste that we have.

Mathematics provides us the tools for solving problems in all of those contexts. So we really need to labour to show our students those different kinds of things and to be thinking hard as we look out into the everyday world. Where does mathematics connect in ways that perhaps we wouldn't expect and that our students need to encounter in the school context?

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