The Secret World of Maths

LINKS:
TedEd on Pi: https://www.youtube.com/watch?v=9a5vHXsUvUw
Jaden Chong recites Pi to 1,800 places: https://9now.nine.com.au/a-current-affair/melbourne-sevenyearold-memory-boy-becomes-sensation-remembering-pi/caf43ef6-dc39-486b-89eb-a79bfba64641
How to count seed spirals on a sunflower: https://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/
The Fibonacci sequence spiral: https://www.mathsisfun.com/numbers/fibonacci-sequence.html
More Fibonacci:
https://www.naturphilosophie.co.uk/fibonaccis-golden-spiral-relationship-maths-nature/
https://mathimages.swarthmore.edu/index.php/Fibonacci_Numbers
NASA’s Starshade: https://exoplanets.nasa.gov/resources/1015/flower-power-nasa-reveals-spring-starshade-animation/
Maths in art: https://www.sciencenewsforstudents.org/article/math-is-muse-for-these-artists

EPISODE TRANSCRIPT
We can find it in shells, flowers, pinecones and snails… it’s needed in sport, construction, space exploration and more… and it pairs very nicely with a sweet, flaky dessert. This is your Squiz Kids Shortcut to the Secret World of Maths—the podcast where we dive into the who, what, when, where, why and how of the big news stories. I’m Amanda Bower.

And I’m Bryce Corbett.

Bryce, March 14 was always a VERY exciting day in my classroom, and at my old school. I taught in America, where you write the month first, and then the day. And so March 14 was written 3/14… and 3.14 are the first three digits of something in maths called PI. That’s p-i, not p-i-e, but the beautiful thing about P-i Day was that dozens of kids and teachers would bring p-i-e to school. I’m talking peach pie, blueberry pie, apple pie… and of course there was the Aussie teacher who also brought meat pies…

I wonder who that was!! Today, we’ll take you through WHAT pi is… HOW else maths is found in art and nature … and WHO has jobs that involve maths…

Listen carefully – there’s a Squiz at the end!

WHAT
Okay, Bryce, you need a piece of paper, pencil, ruler, and an empty cup. I want you to trace around the cup, which should create a pretty perfect circle. Squiz Kids – join in! You can pause until you’ve finished, or just keep listening to Bryce modelling it for you!

Okay… circle is traced.

Now, get your ruler and measure the DIAMETER of the circle… that’s the straight distance across the middle of the circle.

Too easy! It’s 17 centimetres.

Great. Now, I’d like you to measure the CIRCUMFERENCE of the circle… the distance around the outside.

Well, my ruler is no good for that, because a circle is round and my ruler is straight. I’ll just run and get my tape measure.

Stop! No tape measure allowed. Just the ruler, pencil, paper, and cup.

How about a piece of string? I’ll just run that around the circle, then measure the string’s length on the ruler.

Sorry, no string.

I’m sorry, with just a straight ruler, it’s impossible to find the circumference! Right, Squiz Kids?

Well actually, thanks to our friend Pi, you CAN find the circumference of ANY circle, if you have the diameter. I can tell you right now that the circumference of your cup is 53.4 centimetres, rounded to the nearest tenth of a centimetre.

What???

About 4,000 years ago, mathematicians in ancient China, Babylon, Greece and India, all separately started to notice a very intriguing thing about the relationship between the circumference of a circle and its diameter. If they measured the circumference, with a piece of string or something else that I was too mean to give you, and then they divided the circumference by the diameter, they would ALWAYS get the same number.

No matter how big or small the circle was?

No matter how big or small the circle was. The other intriguing thing was that this number was what mathematicians call “irrational,” meaning that it could not be expressed by a fraction. The number was 3.141592653… and those decimal places just went on forever. But if you divided circumference by diameter, you always got that same, irrational, infinite number. Pi.

Wow. Okay, so it obviously comes in handy when you want to know the exact circumference of something. How else is Pi used in real life?

Everything from calculating the volume of lemonade in a can, to the orbits of satellites, to understanding things that involve curves, like electromagnetic waves. I’ve popped a great TedEd video in your episode notes if you’re keen to learn more about Pi, as well as an astonishing video of 7-year-old Melbourne kid, Jaden Chong who spent lockdown memorising Pi to 1,800 places.

Oh I love that kid! So Amanda, thanks to Pi, we can see maths in every circle around us… how else do we see maths in real life?

HOW
Well, one of my favourite places to look for maths is in nature. Bear with me, Bryce, I’m going to ask you to do some mental addition. Squiz Kids, you might want to grab a pencil and piece of paper to play along at home. Ready?

Ready!

Okay, we’re going to start with the number one. The rule we’re following is that you add the last number in the sequence to the number before it. Now, because we haven’t started yet, you’re just adding one to zero.

I like this kind of maths. One plus zero is one.

Okay, so now your sequence has two numbers: 1, then 1. So now you add them together.

One plus one? That’s… Two.

Well done! Now two plus one?

Oh, I see, because in the list we’re creating, there’s a one before the two. So the next number is three.

Beautiful. Now our sequence is 1, 1, 2, 3. So three plus two?

Five… and now I need to add five and three, yes? Eight?

Exactly. Now we’re going to get into bigger numbers faster. Eight plus five?

Thirteen!

Okay, so if you’re playing along at home and want to keep going, hit pause, and keep going until you have at least 10 numbers in the sequence. Then hit play again when you’re ready to hear what Bryce has got. Because Bryce, you’re going to do it too!

Alright, drum roll please… I’ve got: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597

Whoa whoa whoa… you got excited! You went well past ten numbers. Nice job!

Yeah, so doing the maths was fun, but I thought we were talking about maths in nature…

That’s the cool thing about this. Those numbers show up everywhere in nature.

• If you cut a banana into slices, it has three distinct sections
• An apple has five.
• Just about every flower in nature has either 3, 5, 8, 13, or 21 petals.
• The number of seed spirals on a sunflower are almost always a number from this sequence… huge ones can get up to 144 spirals.
• These numbers are also involved in the leaf growth of succulents, cabbages, and tons of other plants.
• It’s in the spirals on pine cones, rings on palm trees, and bumps on trunks of other trees.
• And if you diagram these numbers – I’ve popped a link in your episode notes to show you how to do that – they make a spiral. And THAT spiral shows up everywhere in nature… from nautilus shells to galaxies in space.

But… plants and snails and galaxies surely aren’t aware of maths… so why are they growing that way?

Well, mathematicians and biologists think that in the case of plants, this way of arranging growth – this spiral – probably gives the plants an advantage… either with maximising the space for the leaves to grow, or the amount of light that falls on each individual part of the plant.

So nature is doing cool maths without even realising it…

Basically! Next time you see a sunflower or a cabbage in real life, have a look … and I’ve popped some photos into your episode notes to check it out on a screen, too. This sequence we just explored is called the Fibonacci sequence, after an Italian mathematician working in the middle ages…

I’ve heard of him! And he’s been dead for about 900 years, so you know he’s famous… WHO are people alive today with cool maths jobs?

WHO
Bryce, have you ever done origami?

Of course! The ancient Japanese art of paper folding… I can just about manage to fold a paper crane, if I follow instructions carefully.

Well, if you look on the internet nowadays, you’ll see all kinds of job postings … that means ads for jobs that are available… for people with PhDs in origami, to work everything from designing medical equipment that needs to be swallowed easily by patients…

Cool…

… to sending equipment into space for NASA.

Wait.. origami in space? How could that be helpful?

There are lots of ways, but here’s one cool example. NASA’s New Worlds Mission, which will be taking photos of earth-like planets in space, will have to deal with the problem of light from other stars interfering with those pictures. Enter Starshade, which basically looks like an origami flower that blooms when necessary to create shade for the telescope. I’ve popped a video to a simulation in your episode notes.

Cool! And of course, maths must be used all the time in space exploration – it’s crucial for calculating how rockets take off, orbit, and land. Then there are jobs using maths in sport, looking at stats to figure out your approach to a game… in construction, to make sure buildings and bridges don’t fall down… and of course business… because whenever you use money, you use maths.

And there are some incredible artists out there using maths in their work, too. I’ll pop some images into your episode notes of 3D sculptures that create mathematical patterns when you shine light into them… quilts that represent Pi… and much more. Maths is everywhere, and it really can be quite beautiful.

The S’Quiz
This is the part of the podcast where you get to test how well you’ve been listening…
1. What was the name of the Italian mathematician who described a sequence of numbers found everywhere in nature? ”
2. What’s the name of the Japanese art of paper folding which scientists have adapted to explore space, and make medical equipment we can swallow?
3. What are the first three digits of pi?