What are coordinates?

0:47 Welcome to Maths Is Not Boring by kidopoly.com. I'm Mira! And I'm Finn! If you haven't already, tap follow wherever you're listening so you never miss an episode.

1:00 Today we are looking at something so ordinary you probably use it every single week without even realising it.

1:07 But to actually see this idea, I want you to imagine a completely blank, totally empty, white piece of paper.

1:15 Okay, I am picturing a huge, bright white page. Nothing on it at all.

1:21 Now imagine I drew a tiny black dot somewhere on my blank paper, and I want you to draw a dot in the exact same spot on your paper.

1:32 That is literally impossible. Unless I can look over at your page and copy you.

1:37 Right. If we are in different rooms and you cannot see my paper, how can I tell you over the phone exactly where my dot is?

1:46 Well, I guess you could say it is near the top right corner? Or sort of near the middle?

1:53 But near the top right is fuzzy, and maths loves to be exact. If I just say near the top, your dot won't match mine.

2:02 So I guess I could grab a ruler and measure it from the edge of the page.

2:07 Exactly! But here is the big question. How many measurements do you need to pin down that one single spot perfectly?

2:16 Just one? Wait, no, because one measurement, like two inches from the bottom, just gives me a whole flat line of possible spots across the page.

2:26 Yes, that one simple puzzle, how to pin down a spot on a flat page, sparked an idea that completely changed how we see the world.

2:36 Okay, so if one measurement gives you a whole line of possibilities, you definitely need something more. You only need two numbers, how far across and how far up. Wait, that sounds exactly like when I played battleships with my sister. Or when I look at the squares on a chessboard.

2:53 That is exactly what it is. Or think of a pirate map, where the secret instructions tell you to walk ten paces east and five paces north to find the buried treasure.

3:04 You really just need two numbers to find any spot on a flat surface. It is like a secret code for places.

3:11 We call those two numbers coordinates, and they make up a giant invisible grid that sits behind every single map you have ever seen.

3:21 So who was the first person to actually see this invisible grid?

3:25 The story takes us all the way back to the year 1637, mostly in France and the Netherlands. A long time ago. Who was it? A brilliant French thinker named René Descartes wrote a famous book about joining numbers and shapes.

3:42 Did he draw the first modern grid? Like the one with the perfect crossing lines that we see in school? Actually, no.

3:49 He did not draw the modern grid with two crossing axes. And another incredible French mathematician, named Pierre de Fermat, was having very similar ideas at the exact same time.

4:02 Wait, so two different people saw the idea at the same time, but Descartes gets all the glory?

4:07 Well, the grid we use today is named the Cartesian grid, after Descartes. That is his lasting fingerprint on the world.

4:15 Okay, so how did René Descartes actually come up with the idea for coordinates? Was he drawing pirate maps?

4:23 Not exactly. There is a very famous story about how it happened, but I have to tell you right now that it is a legend. Nobody actually knows if it really happened this way.

4:34 I love a good legend.

4:36 Tell me the story anyway. The story goes that Descartes was lying in bed, staring up at the flat ceiling of his bedroom.

4:44 Oh, I do that all the time. Especially when I am supposed to be cleaning up my room and I just want to lay there.

4:50 Well, while he was staring into space, he noticed a little fly crawling across the ceiling above him.

4:57 I had a spider on my ceiling just this week. I know exactly how that feels.

5:01 According to the legend, Descartes watched the fly and started wondering. How could he describe exactly where that fly was at any frozen second to someone outside the room?

5:13 Because if he just yelled, it is up there, that would not help anyone find it at all.

5:19 Exactly. You cannot just point. So the legend says he realised he only needed to measure two distances from the corner of the room.

5:29 Oh, how far the fly was from the wall on the left and how far it was from the wall at the bottom.

5:35 Yes, across and then up. Those two numbers pin down the fly perfectly.

5:41 No pointing required. That is absolutely brilliant. Even if it is just a myth, it is such a perfect way to picture it.

5:48 Myth or not, what Descartes actually did write down in his 1637 book called La Geometrie was massive.

5:56 What did he write that was so huge?

5:59 Before him, people thought geometry, which is shapes, and algebra, which is numbers, were totally separate things.

6:07 Like two completely different subjects at school that never ever talk to each other.

6:13 Yes, but coordinates built a magical bridge between them. The Cartesian grid suddenly connected the two worlds.

6:21 Wait, I am confused. How does a grid build a bridge between shapes and numbers?

6:26 Because suddenly, a shape like a circle or a triangle wasn't just a picture anymore. By putting it on the grid, you could write the entire shape out as a set of numbers.

6:37 Oh wow! So you could literally describe a perfect circle to a friend over the phone using just numbers, and they could draw it exactly right.

6:46 Yes, you turn the shape into coordinates. The picture becomes pure math. The numbers paint the picture for you.

6:54 But hold on, what if you are not on a flat ceiling or a flat page? What if you are on a giant ball, like the Earth?

7:02 That is a brilliant question, Finn. You still use coordinates to pin things down, but they curve around the ball.

7:08 Like latitude and longitude lines on a globe.

7:11 Exactly. It is a slightly different grid, but the idea is the exact same. Two numbers find the spot. But the simplest, most magical version is the flat Cartesian grid.

7:24 So, every time my parents use a map on their phone to find a restaurant. Is that Descartes' idea?

7:31 Yep. Every single time a phone map drops a little red pin, it is secretly using coordinates to say exactly where that spot is on the grid.

7:42 It feels crazy that an idea from 1637 is basically running our GPS today. It is hiding everywhere.

7:50 It is. And speaking of Descartes, here is a really fun fact about him. He was a philosopher who said the famous words, I think, therefore I am. But he also loved sleeping in. Wait, really? A famous genius who slept in? Yes. Ever since he was a kid, he had frail health. So his teachers let him stay in bed until noon.

8:16 He did his best thinking in bed. I need to tell my teachers about this immediately. It is for science.

8:23 I'm sure they will love that excuse. And it is probably why the legend of the fly on the ceiling feels so believable. What about the other guy, Pierre de Fermat? Fermat was actually a lawyer by day. He just did brilliant mathematics in his spare time for fun, often writing in the margins of his books.

8:44 A lawyer doing world-changing math as a hobby. That is wild.

8:49 It really is. The idea they both saw changed the way we understand the world. Space itself became something we could measure and map with just two simple numbers. Alright, Finn, quiz time! Let's see how much of this invisible grid stuck with you.

9:06 Okay, I am ready. Bring on the questions.

9:10 First question. What year did Rene Descartes publish the book about this idea? Next one. What kind of bug is famously part of the legend about Descartes staring at his ceiling? Question three. Who was the other French mathematician who had very similar ideas at the exact same time? Here's number four.

9:41 What do we call the two numbers that tell you exactly how far across and how far up a spot is? Last question. Because of Descartes, what is the invisible flat grid named today? Great job! Let's see how you did. The first answer is he published it in 1637. For question two, the legend says it was a fly on his ceiling.

10:14 Number three, the other brilliant thinker was Pierre de Ferma. For question four, those two numbers are called coordinates. And the final answer is, it is called the Cartesian grid, named after him.

10:28 You know, I don't think I will ever look at a map on a phone the same way again. It is all just numbers pinning things down.

10:36 It really is. The next time you see a blank page, just remember that every single spot on it already has a secret name, waiting for you to find it.

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11:18 Thanks for exploring with us. See you next time on Maths Is Not Boring. Bye everyone!