What is a labyrinth?

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.

0:59 You know, Mira, with Halloween coming up. I was just thinking about the absolute spookiest feeling in the world.

1:06 Oh? Are you talking about the feeling of being completely and totally lost in a giant corn maze?

1:14 Huh, exactly. The sun is going down, the corn is super tall, and every single muddy path looks exactly the same.

1:25 It is a great Halloween shiver. But what if I told you there is a mathematical trick that means you never, ever have to be lost in the maze again?

1:34 Wait, really? You mean without using a map or flying a drone over the top?

1:40 No map, no GPS, and no cheating. Just one single mathematical rule that works almost like magic.

1:48 Is it that really old trick? The one from the ancient legend with the monster. You mean the story of Theseus and the Minotaur? Yes! The Minotaur was that giant grumpy creature with the head of a bull, right?

2:01 That is the one! In the ancient Greek legend, the Minotaur lived right in the centre of a gigantic, twisting labyrinth.

2:09 And the labyrinth was designed so that anybody who walked inside would just wander around those twists and turns forever.

2:16 Exactly. But the hero, Theseus, had a brilliant plan. Before he walked into the dark maze, he tied a ball of thread to the heavy front door.

2:26 Oh, I love this part. He just unwound the string as he walked deeper and deeper into the labyrinth, letting it trail behind him.

2:33 And when it was time to leave, he did not need to know the way. He just followed his own thread straight back out.

2:40 Haha, it is such a good trick. But I definitely do not have a giant ball of thread in my pocket when I go to a corn maze.

2:47 And that is exactly why mathematicians found a way to escape that needs absolutely zero thread. Wait, how do you solve a maze with literally nothing? It has a real mathematical name. It is called the wall follower rule, or the right hand rule. Okay, the right hand rule. What do I actually do? Imagine you are standing at the entrance of a giant maze looking in.

3:12 Just reach out and put your right hand flat against the wall next to you.

3:17 Okay, my hand is on the wall.

3:19 Now start walking. The only rule of this math trick is that you can never, ever, lift that hand off the wall.

3:27 Wait, even if the wall turns a really sharp corner.

3:30 You just walk right around the corner, sliding your hand along the leaves or the stone the whole time.

3:36 But what if the path goes totally dark and I walk all the way down a creepy corridor and it ends up being a dead end?

3:43 You do not panic. You just keep your hand touching the wall, trace your fingers all the way around the U-turn at the dead end, and walk right back out.

3:53 But wouldn't I just be walking back the exact same way I came?

3:57 Only on the other side of the corridor. You are basically tracing the entire shape of the maze's outer wall. Oh, I see.

4:05 Because the maze is just a bunch of super long walls folded up into a small space.

4:11 Exactly. If you just trace the edge of a folded-up shape, you have to eventually hit the exit.

4:17 Even if the path twists around a hundred times, I'll just follow every single twist.

4:23 You might walk down every single wrong path first, so it won't always be fast. But mathematically, you are guaranteed to get out. Hold on, Mira.

4:33 I just pictured something ordinary that completely breaks the trick. Ooh, tell me, what did you notice? What if there is a wall in the middle of the maze that isn't connected to the outside edge at all?

4:46unknown Ha ha!

4:46 You found the catch! Mathematicians actually call that an island.

4:51 Because it is literally an island of wool standing all on its own in the middle of the paths.

4:56 Yes, a maze with no islands at all is called simply connected. In a simply connected maze, the wool follower trick always works.

5:06 But if there is an island, and my hand accidentally touches it, wait. I would just trace the shape of that island, around and around.

5:15 You would loop endlessly. You'd just walk in a circle around it forever, trapped by your own math rule.

5:22 Whew, that is a terrible trap. Did people actually build mazes like that on purpose?

5:28 Oh, absolutely. The oldest surviving hedge maze in Britain is at Hampton Court Palace near London. How old is it? It was planted around 1690 for King William III and Queen Mary II, with thousands of tall bushes. And does it have islands to trick people? It does. It was specially designed to mess with people who tried to use the wool follower rule.

5:52 So if the hand trick fails when there are islands, how do mathematicians really solve complicated mazes today?

5:58 They use something called graph theory. They just imagine every single junction where paths cross as a little dot.

6:06 Wait, dots? Like a giant game of connect the dots.

6:10 Exactly. And the paths between those junctions are just lines connecting the dots. It turns the maze into a clean network. So you don't even have to look at the walls anymore, just the dots and lines. Right. But the hand on the wall trick is still used every single day by things that aren't even human.

6:29 Wait, what? Are there animals doing math in mazes? Not animals. Robots. Specifically robot vacuums. The little round robots that drive around cleaning the floor? Yes. Your house is basically a giant maze to them, full of furniture islands and wall edges. That is so sideways. So when it bumps into a chair leg, what does it do?

6:53 It uses a version of the wall follower rule. It touches the edge, follows the shape around the obstacle, and keeps going.

7:01 So every time my robot vacuum cleans the living room, it is doing maze math. And I guess video game characters probably use it to find their way through dungeons too.

7:10 Alright, Finn, it is time for the quiz. Are you ready? Oh I am so ready. Let's do this. First question. In the ancient Greek legend, who used a ball of thread to escape the labyrinth? Next one, what is the name of the mathematical trick where you never stop touching the side of the maze? Question 3. What do mathematicians call a wall that is not connected to the outside edge of the maze?

7:50 Here's number four. The famous hedge maze planted around 1690 is at Which Palace near London? Last question. What kind of everyday machine uses maize math to clean your house? Great job! Let's see how you did. The first answer is the hero Theseus. For question two, it is the wall follower rule or the right hand rule.

8:23 Number three, the answer is an island. Question four, that is the maze at Hampton Court. And the final answer is a robot vacuum.

8:35 I am honestly never going to look at my robot vacuum the same way again. It's basically a little hero solving a labyrinth.

8:44 Next time it bumps into a wall, just imagine it is escaping a minotaur.

8:48 If you love learning about maze math with us today, please leave us a five-star review.

8:54 Yes! Just scroll down and tap the stars. It helps other kids find the show so they can escape corn mazes too.

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9:21 See you next time on Maths Is Not Boring. Bye.