Shapes and Smoke Rings - EMF 2026

Uh right. Good uh good afternoon everybody. Um I am I tell you what I'm going to do is I'm going to introduce myself quite slowly uh so that we can allow a few more people to come in. There's a few more people sort of on the way I think. Um and so I think probably yes probably before I tell you anything about shapes and smoke rings which is what we'll be uh be doing this afternoon. Um, I'm going to tell you a little bit uh more about myself. Probably the easiest way of understanding who I am is to say I'm a mathematician. Uh, which means um that I studied math at school. Um, and then I went to university and I studied maths there. And then I've done some things with math since. Um, and now I spend a lot of my time um actually uh I spend quite a lot of time in schools and at various other places, science festivals, this kind of thing. Um, just showing people the bits of maths um that I think is most fun and exciting, which is is really great fun. So, it's really lovely to be here um on this. I'm I'm so glad it's slightly cooler uh now than it has been. It's just perfect weather. It's brilliant. So, it's very exciting to be here. Um, so uh so that's me. I've done a little bit on number file is a YouTube channel all about maths. Um, and very occasionally uh on uh BBC Radio 4. I imagine none of you are listening. Thus, is fine. Uh, and shapes and smoke rings is actually I still don't think I'm going to tell you too much about it until we've warmed our brains up a bit. Actually, warm that's not the right phrase, is it? Warmed up. We are already warm. Uh, we've woken our brains up a little bit with a puzzle. So, I'm going to give you a puzzle. Um, and your job is to your job is to wait for me to put my clicker on. There we go. Your job is to see if you can join up um identical symbols on the screen um with a line. However, there are some rules. The rules are that those lines, they cannot cross each other. Um, and they also cannot leave the box. So, you can see that that green one is right down against the edge of a box. Uh, it's there for a reason. You can't go around it. You also you can't go over the shapes as well. Um, and actually the question I've got for you is do you think this puzzle is possible? Um, or do you I don't want to know now. [laughter] Um, rule one, hands up. No, we're not in school. It's fine. Um, so the question, you're going to have a minute to think about it and talk to person next to you. Um, is do you think this puzzle is possible? Would you think it is not possible? I'm going to give you a minute to think about it. You don't have to draw it. You can just do this kind of thing if you want to. Um, a minute or two while we wait for more people to come in. Have a go. What do you think? Possible? Not possible? Have a chat. That's fine. Chat to the person next to you. Even if you don't know them. Okay, come in. Welcome. Don't worry, you're not late. It's fine. Just find yourself seat. And I'm It might make sense. There's not many of you. It might make sense to sit around here. Um you can hide at the back if you want to, but yeah, probably makes sense to be there. Oh, you've got a an ice lolly. is exactly what I need. Oh my gosh, I'm jealous now. Right, we've got people thinking. So, the puzzle that people are thinking about, people who've just come in, um, is they are trying to to work out or decide whether they think this puzzle is possible or not possible. So, we're linking up identical pairs um without lines crossing and the lines can't leave the box. So, we think it's possible, not possible. Um, I think what we will do, you've got a you've got kind of 10 seconds to make a decision, you three. Uh we're going to do a hands up vote and I I can literally count you all. So no one's getting out of voting, right? I know if you're voting or not. Um so everybody's got to vote for either possible or not possible uh for this puzzle. We'll see what you think. So grown-ups too. Uh you do also have to vote. Uh so hand up if you think that this is impossible. If you think this puzzle is impossible. [sighs] I've got two hands from over there. This person is extra sure. But it's not everybody, I don't think. Hand up if you think it's possible. If you think this puzzle is possible, there are about three or four who think it is possible. Um and so I would say that's sort of 20% versus 80%. 80% impossible. And you know when I asked people this question that's what people normally say. They normally say to me yeah I don't think this is possible. And when I first saw this as an adult right and a mathematician not very long ago um I thought it was not possible. But in fact as some of you might have spotted there is indeed a solution. There is a way of doing it which is quite nice quite satisfying isn't it? Yeah it's quite surprising. And there's a reason there's a reason that I start this talk uh with this puzzle. And in order to explain that reason, I am going to show you a much easier puzzle. Now, so it's exactly the same rules as last time, but it's much much easier. And this time, you don't need to say anything. I just want you to put your hand up when you see a solution. So, as soon as you see a solution, you can uh you can have a stretch and put your hand up again. Even even adults, thank you very much, grown-ups as well. Brilliant. Really good stuff. Yeah, this is really easy, isn't it? You're probably thinking, why is why is she giving us something so easy? Um, and there is there's a reason for that. So, I am going to move this blue one a bit. You don't you don't have to do anything now. I'm going to move it. And I think you'd still tell me that's fine, wouldn't you? You clearly just have to bend the lines a bit. And even if we move it down here, it's it it's the same thing, right? I think mathematically it's the same puzzle. We've just had to stretch things a bit. The way it is connected is is the same. And actually, if we move it down here, that's the same thing. This is also even the same thing. It's It's totally doable. So is that and so is that. Oh, what's that one? Somebody younger than 18. What's that one? Is that the really tricky one? That's a really tricky one we saw at the start, isn't it? Um, and the point that I'm trying to make is that the really easy one and the really difficult one, uh, they are essentially they're the same puzzle, right? Mathematicians will say they're the same. Um, we've just had to stretch things a bit. And there's an area of maths called topology, which some of you will know about. um and and some of some of maybe the ones of you that are a bit younger, maybe if you go to university and study maths um you will meet it. And it's essentially it's all about shape. Uh and it's all about um what kind of what stays the same when we stretch and we deform shapes. Um and really topologists, they're really interested in how things are connected. Not really where they are, right? So not really where they are in space, not really what they look like, but how things are connected. Um, and we're going to do we're going to kind of dip our toes into a little bit of topology and and some other fun stuff um in in this talk. Um, and uh and we're essentially it's it's kind of an excuse for me um to show you my top three shapes. Right. So, I've got I mean I've got a top 10 shapes, but we've not got all day, right? So, we're just just going to go top three shapes, third favorite, work our way up towards uh my ultimate favorite shape. Uh it is more exciting than I'm making it sound. Uh we and in each case we're going to look at the properties of the shape a bit like a a topologist. Um and actually but before I do that before I conclude this when as soon as I put this puzzle up even before I asked the question uh some people went oh it's impossible and and and they were very certain. There was even somebody with two hands up which was uh extra certain. Um yeah you're over there. Um and do you know why I think that is? I think that's because you might be confusing it with a very famous puzzle. There's a very famous puzzle which is a bit different um which asks a slightly different question. It says instead of can you join each identical symbol. It says can you join say the top blue one can it be joined with all three at the bottom and can the top green one be joined with all three at the bottom and the same for the yellow one. Um without lines crossing like for example this is the blue one would have to go with with all of those ones at the bottom and then all the green and and the yellow. Um and that is not possible without lines crossing. That is not possible um on a flat surface. Although you might be looking at it now and not recognizing it because usually it's it's kind of uh it's kind of shown to us in a slightly different form. So usually it's shown to us like this as the utilities puzzle. Um the idea is can you join each house with the three utilities um that it needs. Uh not possible on a flat surface. However, here we go. Possible on the surface of a mug. Um and so if you want to uh children, you need permission from your parents, but if you want to get a mug from your cupboard at home and a dry white pen, you could draw the little symbols on. you could see if you can work out how you can uh do the puzzle without lines crossing. Um it's also possible on the surface of a donut. They are to topologists they are this the same shape because I said what they care about is how things are connected, right? And these two shapes they are they're connected in the same way. Um if you took the cup and you kind of but imagine it's play-doh, imagine it's plasterine. Imagine you remold it. You you don't have to cut it. You don't have to um you don't have to do any cutting or sticking and you can remold it into uh into the donut. So, it's connected in the same way. Topologists say um they are the same shape. Should we do that again? I quite like that. Oh, lovely. It's going back again. That's nice. I find that very satisfying. Anyway, so do go and do that as an extra challenge. Mas gear, you can buy them online. I don't work for mascara. I'm just uh I'm just showing you that because you might be interested. Um or you could just draw it on yourself. That would be equally fine. However, we are going to crack on with my three favorite shapes. It's my third favorite, working our way up towards my ultimate favorite. Um, and actually the f third favorite allows us to do a particular magic trick. Right. So, I am going to describe the trick. Um, then you can all have a go at the trick. Um, oh, that should not it's No, that's fine. We're all good. Um, and then I'll explain what it's got to do with maths. And if you think you've seen this trick before, then just kind of keep very still like that like a statue while I'm describing it. Once I finish describing it, you can you can all have a go. Go wild. That's fine. Um, right. So, your job is to try and get your arm from this position to that position. Um, without just turning it over. That's very easy. Uh, that's not a trick. Uh, you have to kind of pretend that your arm is like in a cast. Okay? So, it's broken. You can't rotate your wrist. That's not okay. You are welcome to rotate your elbow. That's completely fine. You don't need to do backstroke. Anything that looks like a swimming stroke, this is not a solution. You don't need to get out your seat. Don't do anything we've not risk assessed. Uh, right. See if you can do it. So, from this position to that position without turning it over. Off you go. One minute. Talk to person next to you. See if they can do it. Everyone can have a go. Everyone have a go while I drink some water. It feels like you're all waving at me in a kind of mathematical way, which is nice. This is bizarre. [laughter] >> H got some solutions in the room. And you know, we've got some people really trying hard to work out the solution, which is nice. Um, we've got even some grown-ups who are really unsure what to do. [laughter] Okay. Um, let's see if I've got anyone who's done it. I think I saw someone over here who might have done it before. Saw how to do it. Can I see anybody? I can see some people I recognize who might know how to do this. Uh, which is nice. And some people I don't recognize. What we all will do is Hey, what? Should we do it all together, right? Do you want Should we just I think there's at least one or two people who've worked out how to do this. Um, let's do it all nice and slow together. Um, we'll do our palm out p arm out, palm face up like this. And we'll start um by doing a 90 degree bend at our elbow. So, our fingertips are pointing upwards like this. Lovely. It's so nice. You're my my maths robots. It's lovely watching a room full of people doing the same thing. Lovely. Then we're going to do another 90° bend. So, our fingertips are pointing across our bodies like that. Yeah, that's going to hurt. Don't do that. That way. And then you're going to do another 90 degree bend at your elbow. So your fingertips are pointing this way. And then lots of you have worked out what to do. Just the same thing again. Yeah. Up to the top. Over to the side. Round to the front. There you go. Do you want to have a little practice? Yeah. Super fun. Up to the top. Over to the side. You could do both arms. Can anyone try both arms same time? This is your If any of you are going to be dancing later on, this is the dance to be doing. I'm going to be looking out for it on the dance floor. Yeah, we've got someone doing two arms there. I love it. Excellent stuff. Right. So, this is this is good fun. Uh but somebody is probably thinking um I thought this is about maths. Where's the maths in this? So, we'll have a little think. Um so, essentially when I'm doing this trick, the shape that I'm thinking of is a sphere, right? A spherical shape. Um a sphere because um when you're doing this trick, you can imagine that your elbow is the center of the sphere. You can imagine that your fingertips are always on the surface, always on the very surface um of the sphere. Um, it's it's like your fingertips are tracing out a path on the surface of the sphere. And the distance, of course, from your elbow to your fingertips, it doesn't change, right, when you do the trick, unless you break your arm or something, that's always the same. And and of course, that's the same for a sphere, right? So, a ball shape for people a bit younger. Um, and uh, so the distance from the center of the sphere um to the surface of the sphere is always the same, right? It's always the same distance. I mean, that's the definition of a sphere, really, isn't it? Um, so that's that's what's going on. Um, and so I say yes, it's a sphere whilst showing a picture of not a sphere on the screen because as you might know the earth, not a sphere. Um, but not far off. Not far off. And it makes some nice images for what we're going to do. So we're going to pretend, if that's okay with everybody, we're going to pretend that the Earth is a sphere. And we're going to imagine that you've dipped your fingertips in some pink paint and they start here kind of on the equator um off the uh off the west coast of a Africa there. Um, and let's just see what this path looks like that we've just done with our fingertips. So, we're going to go up towards uh the North Pole. So, it looks something like this. And then we're going to go 90° over towards the east. So, it's going to go over there. Uh then we're going to do another 90° bend. So, we're joining up that pink triangle. Um and then we just went over that pink triangle again. Job done. Um now, one or two of you might have been listening really carefully. Um and you might have heard me say, uh 90° bend, 90° bend, 90°. In other words, right, those three the three angles in that pink triangle, they are all 90°. Uh, now I am sure that there are lots of you who a very long time ago uh learned something at school about triangles and angles uh inside and there are some of you maybe who maybe I don't know how old you you maybe maybe haven't maybe you teachers may have told you by now who knows but if they haven't they will do soon. Um, and this thing about 180 degrees. So, you go to school and they say, "Right, the angles inside a triangle add up to 180 degrees." And then you see this and you're like, "Hang on, three times 90, that's 270." Uh, what's going on? Um, and essentially, as lots of us probably know, if you take, uh, the, uh, a triangle and you draw it on something that is curved, um, spherical like that, is not a flat surface, um, then you'll get more than 180 degrees. Essentially, the rules of geometry, uh, just completely change. So, if you're not on a flat surface, everything goes a little bit wacky, right? There's some fun stuff about parallel lines. I'll be a fond of two of you will be reminding you of like maths degrees I imagine now. Um but anyway, geometry of a flat surface, very different from the geometry of um something that is curved. Um and so we we draw a triangle and we get more than 180°. Um and so the 180 degrees only works for a flat surface. And actually if we drew a triangle on something that curves the other way like that, um then uh we're going to get we're going to get less than 180°. Um and that's kind of why I like I like the sphere because it allows us to do this trick. This is what you're doing with your fingertips when you're doing this trick is you are effectively you're you're drawing a triangle with more than uh 180 degrees in it. Um and occasionally one or two people have seen this trick and it frustrates me. And do you know do you know why they've seen it? They've seen it on Tik Tok or some other social media. Occasionally young people I show this to oh yeah I've seen that and do you know just so it went viral on Tik Tok a couple of years ago. Um and they didn't do the math. So all these people around the country doing this trick having no idea that what they were doing was uh drawing a triangle with uh three 90° angles in it, more than 180 degrees. So I thought we've got to do the maths. We've got to do the maths of the viral trick in the talk. So that that's why I like the sphere really. Um we are however um we're going I say we're going to move on to my second favorite shape. say that. But actually, just before we do that, I'm going to address uh the the elephant in the room, the question in the room, because there will be one or two people who are thinking, "But that's not a triangle." Because and it's probably you with your hand up because those those lines are not straight, right? They look kind of curvy. I've been told a triangle's got straight lines. Um this one in particular, people people are not happy uh with that. Um so the definition of a straight line is is the shortest distance between two points. Um, and if you wanted to go from, is it just north of Australia? Yeah, whatever. If you want to go from there to the North Pole, um, I mean, you would just go due north, right? That would be the, as the crow flies, the shortest way to do it. You just go due north. So, that is the shortest. I mean, I advise you don't. A lot of sea in the way. Um, it would take a really long time, but but that that is what you would do. So, that is the shortest route. Um, it just doesn't look like what we're used to straight lines looking like, but it is a straight line. It's something called a geodics. If you're interested in kind of like, you know, why do airplanes not fly what looks like a straight line? Why do they fly up towards the poles? Um there's all sorts of interesting stuff in that. It's all connected. So this is a a straight line um on the surface of a sphere. So they are straight lines. It is a triangle. Um it does have 270 degrees. Um but we are going to move on swiftly on to my second favorite shape. Here we go. Which is not this. This is a rectangle. Some of you have seen that before, I imagine. Um, [laughter] but if I take my rectangular strip of paper, um, and I I'll do I'll do this under the camera so you can see what I'm doing. Um, so I take my rectangular strip of paper and I get some sticky tape or some glue, some cellar tape. Um, and I do this kind of thing and I stick my cellar tape there. Um, then I get a loop. Maybe I'll call it a loop. I think some of you might call it a cylinder without without ends. That's fine. Um, and that's kind of nice, but actually also still not my second favorite shape. Um, but if just before we sell tape it, if we take one end and we turn that end over and then we sell tape it, then we get my second favorite shape, uh, which is the mobius loop. So, it's like a loop with a little twist in it. Um, it's called the mobius loop. There we go. Um, and here's one. Here's one I made earlier in true blue style. There we go. Um, and actually to think about the Mobius loop, um, and find out what's interesting, we're going to really quickly whiz back to the normal loop, right? the standard loop. And I want you in your head to just imagine. You can just keep it in your head. Um, not that you're being rowdy in any way, but don't shout out. I'm joking. All right. So, take a pair of scissors and we can cut. Imagine I'm cutting a line down the middle all the way round. Just in your head, imagine what you would get. Can you nod at me if you are imagining two loops that are half the width of the Thank you. The two people nodding. Three people. We've got We've got more people nodding. some grown really gentle nods from the grown-ups over there. Thank you very much. Excellent. Um, so that's what we'd expect, right? So that's what we imagine to happen for the normal loop. So we are going to do that, but we're going to do it for the twisty loop, the mobious uh loop. Um, because there is something interesting you can do with the two loops that you end up with, the two halves that you get. Um, and [snorts] if you do this at home, young people or even older people, um, what I advise you do is you make a little fold like that. Um, you do a little cut into your fold. Um, and then you get your scissors in there because I have seen people even even adults going kind of wild and it all just goes wrong. So, be real care really careful. Um, and you just got to start cutting down the middle. It's a little bit fiddly. You might have to turn it over. You've got quite a lot of cellar tape uh to go through. Oh, there we go. My scissors have got stuck already. There we go. And I've got super scissors. Uh, keep cutting on this side all the way around. And we'll get our two loops. Um, and we'll see what we can do with it. So, I'm cutting it all the way down the middle. We'll get our two loop. Oh, what did I not just Did I not just cut that down? Did I cut that down the middle? People at the front, were you watching? Did I have I dropped a bit? Is there a bit on the floor? No. I don't know what's going on. That's weird, isn't it? It's kind of fun, isn't it? Um I imagine for some of you, this is not the first time you've seen that, but we could pretend that it is, right? And the time the first time that you see this, um it's you know, it just blew my mind the first time I saw this. This that is as far as my acting skills go. Um, this is what happens when you cut the Mobius loop uh down the middle. You just get this one big loopy thing. Um, so I guess it's the shape you can't cut in half if you uh if you cut it down the middle. Now, if uh the penny has not dropped as to why that happens, the thing to do when you go home is before you cut your I'll just show you how to do it again. Actually, if you want to see. So, just before you sell tape it, take one end, turn it over, and then sell a tape. And just before you cut it down the middle, the thing to do is to take your pen and start drawing the scissor line on and start drawing on one side and keep going all the way around until you get back to where you started. And you will notice that without trying to, you will have ended up drawing on both sides of the piece of paper. Now, I've not done all of it. I've only done a bit of it, but there we go. Um, so without trying to, you've drawn on both sides of the piece of paper. Now, imagine if you did that for the normal loop, right? The standard one. there's no way that you're going to draw on the inside unless you deliberately go over the edge. Um, and uh, that that's kind of why this happens. So, I think if you draw the scissor line on, this kind of being on both sides at the same time thing is really important. So, draw the scissor line on, notice you're on both sides at the same time. Uh, and actually what topologists say is they say the moious loop has only got one side, right? That that's its special property. Um, this being on both sides at the same time, it's only got one side. Um, so you draw the line on very slowly cuts and the penny might drop. You might begin to see why. Um, we just ended up with the one uh big loop. Um, so I I do like the mobus loop very much. Um, it's my it's my second favorite shape. Um, but it does get a little bit better than this, right? So we can do some slightly more fun stuff with it. Um, and in order to explain the really fun thing, I'm going to have to very quickly whiz back to the normal loops. Can you see here? So we've got two normal loops and they are cellotap uh two loops. I shouldn't call them normal. It's two loops and they are cellar taped at right angles um at 90°. You can see there's like a right angle gap there and there and that kind of thing going on. And what I am going to do is I'm going to cut this one down the middle all the way around. And I'm going to cut this one down the middle all the way around. Um and we will end up with one thing. So just like last time, it'll be one big connected thing. Um and it is your job with the person next to you to decide what shape you think it will be. Uh and you've got the time it takes me to cut this up. So off you go. I will cut this one up. Uh, what shape will we get? You may you may speak to each other. Right. So, do this one first. Oh, it's frozen. It's not happy. I'm doing things, but the camera is not telling me I'm doing things. There we go. That's better. Um, so I'm cutting down the middle. I'm just doing the first one all the way around down the middle. We go. We are halfway. We're at the halfway point here. There you go. Just about. Um, and I tell you what, shall I take a guess? I'm going to take guesses from anyone under 18. Uh, and it's like the reverse of a pub. Um, so if you're under 18, you don't have to show ID. If you want to have a guess at what you what shape you think we will get when I cut this second one down the middle. So, I'm going to cut this second one down the middle. Um, what shape do you think we might end up with? Do you want to have a go? Front line. You don't have to. So, we've got Mobius loop. I'm going to take three different guesses. Maybe two cuz there are only two people under 18. We'll go for two different guesses. What's your what do you guess? >> Maybe like >> maybe a circle. So we've got Mobius loop. We've got the guess of circle. We've probably got some other guesses in our heads. Um we will see. We will see what we end up with. Um and I'll tell you what's interesting is this is the last one I've got to do. So this is going to be a line of symmetry. Um and that's so that's going to be a line of symmetry, isn't it? We saw some right angles at the start. So that might give us a little bit of a clue. So I'm going to cut. So, when you do this at home, you take two uh normal standard loops and you cut them down the middle all the way around. I should probably do it that way. Um then you get two normal loops, cellar tapes at right angles. Cut down the middle all the way around. You get you get a square. There we go. That's quite nice, isn't it? It's quite lovely. It's I find that very satisfying. It's a square. It's lovely. And actually, did you see when it was all cellar taped together, it looked like a cross shape, didn't it? And we saw we saw four right angle gaps. And [snorts] you can Can you see where they've gone? One, two, three, four. Boom. Nice. So, it kind of makes sense. But it does get I've got to be honest, it does get a little bit better than this. It gets a little bit more exciting. And because if instead of having two normal loops and cellaraping those at right angles, if we take two mobious loops, that's the twisty ones, and we sell tape those at right angles. And this is really important. You have to twist one of them clockwise and the other one anticlockwise. Right? Can you remember that? So twist one of them clockwise, one of them anticlockwise. If we take those two mobius loops and we sell tape those at right angles and we cut both of those down the middle uh then we get uh what is quite possibly the most romantic shape uh in maths which is nice. Uh it's two hearts that are in celinka which is lovely and actually you can see can you see the right angles at the bottom of the heart um and the right angles in the kind of iny bit at the top. There's probably a technical term but I don't know. Um, that's your four right angles and actually they're pointing in different directions because of the twists um that we put into the Mobius loops. The interlinking bit I'll just I'll let you I'll let you go and think about that's tricky. Um but anyway, so really lovely. So I would love it if some of you go home and try that. And actually what I've done um for the adults in here who get easily confused, I've made a worksheet, right? So I've made an instruction sheet. I'm going to give you a link at the end. So if any of you families or anyone else wants to teachers maybe in the room, I don't know, want to go home and do this with somebody um please do. I'd love it if you did. Um, you've got I mean we forgot how long have we got now? Seven months to practice for Valentine's Day. That's all you have to do, right? Pair of Mobius loops and a pair of scissors. Job done. Very easy. Um, right. So, that's the moious loop. We're going to move on. It's not my favorite shape. My favorite shape um is something to do with this. It's not this. This is a cylinder. We've seen that already. Um, but if I stretch out my cylinder and I join up the ends, what do I You can just say out loud if you want. What do I get if I join? Anyone at all. Anyone can say what do I get for stretch it out and try and join these ends up. >> Donut. Taurus. We've got all sorts of words. You want to go for it? Yeah. A circle. Some really nice guesses. The circle is a really nice guess because what you've done in your head is you've imagined you've imagined exactly the right shape. You probably imagined um the circle shape, but because it's three-dimensional rather than flat, we're going to give it a different name. Um somebody said donut, which I mean you are nothing if not predictable. That's fine. Um so I'm joking. If you said donut or you thought donut, your brain did the right thing. Well done. Uh, but we don't call it a donut. We call it a Taurus. Thank you, whoever that was. Um, so Taurus is the name of it. Um, and a Taurus is my favorite shape. And the reason it's my favorite shape is there are some mathematical and scientific properties. Um, that means that if hypothetically speaking, I were to fire a Taurus of smoke across the room, um, it would hold its form, uh, for a really long time. Um, it's a very, very stable, that's the word we're going to use, a very, very stable shape. if it was kind of a different shape, it would have different properties. Um, and so we're going to see that. So that's what we're going to do. Um, and essentially, um, your job will just be to enjoy it, which is it's a nice and easy job. Um, and in order I'm sure none of you will I mean, I'm going to do the rules anyway because I just always do, but I'm sure it won't be an issue. Um, but in order to allow other people to enjoy it, just make sure you don't put your hands up. Um, don't disrupt it. And we'll see how far we can get this Taurus of smoke to go. If we can get it to It's quite warm in here, which I'm a bit worried it might up. Um, but if we can get it to kind of the the big um metal things in the [laughter] middle, there's probably a better word for that as well, but the big thing in the middle. Um, that is that's great. That's like round of applause worthy. If we can get it beyond that, that's incredible. If we can get it towards the camera, I don't think I'll get it right. I might get it to the back. I'm not sure. If we can get it towards the camera, that is just go wild. That would be incredible. Um, so that's the idea. That's what we're doing. Um, and just um, so you know, so we're calling it smoke. That's the easiest word to say. Um, but it's inert. So it's not really smoke. It's kind of it's like a sugary solution um, and a heating element and it kind of breaks down to make it look look a bit it's like a smoke effect. Um, so it's inert. It doesn't affect anybody with asthma and we should be all good. Um, I think we are almost ready to go. Um, and we will see it float across the room. We'll see it hold its shape. And after we've had a go at this, then we will think about the reasons um why it is so stable and why it holds its form um really really well. And I'm just going to identify. We've got a camera there. We've got a camera there. I wonder if I can get one to that camera and one to that camera. That would be brilliant. Right, off we go. Um so let's get these smoke tauruses to vortexes in action. Okie dokie. Right. We ready? So, let's go for the middle. Three, two, one. Oo. Oh, it's gone down, not up. Interesting. [applause] There we go. Nice. [cheering] Okay, let's try and have another one. Let's see if I can go a little bit further this time. Let's go this way. Right, ready? Three, two, one. I don't know why it's going down. Oh, it's still going. [laughter] It's almost getting there. It's not too bad. Let's go across the room. Oh, lovely. [applause] Let's go across the room. Let's try and go this way. Right. Ready? Three, two, one. Oh, that was less good. We'll try that one. Oh, no. It's still kind of there. It's kind of there, isn't it? Floating around. We'll do another one in a little bit. It's having a The smoke machine's having a little break and then we will try and we'll try and do a couple more in a second. Um, so we have seen Did it get to the back? The one when everyone went whoop. Did it actually kind of almost not It's not bad. It's a big room. I think we did very well. It's a big room. Um, right. So, what you've seen is you've seen my smoke cannon. That's this thing. It's a garbage waste basket in case anyone is interested to make your own. um garbage weights basket and I uh this hole is covered with tarpolin um the hole that's in the the basket and this hole I cut in because you need a little bit of uh like a margin essentially. So I cut that hole in. So if you want to make one yourself that's what you do. Um and this tarpool in has to have enough give so you can give it a good old whack and it will um it will create the smoke ring. And actually what's happening is you saw me punch the back of the smoke ring. Um, and what I was doing was I was pushing the smoke, that orange stuff, um, towards um, the hole at the front. Um, and essentially the smoke that is in the center um, of the circle is a higher pressure than the smoke around the outside. And what that does is it means that it pushes the other smoke out the way. Kind of like this. So if my arm could carry on, I'd make a little circle um, like that. So what we've got is kind of at every angle around the circle, we've got a little little circles being formed. Um, so the smoke particles are basically making a circle. Um, there you go. That's that circle of circles. Um, but we are going to try and give it one more go to see it in real life. Let's see if we can do it again. That last one I was I was not happy with that last one. We're going to we're going to do that one again. See See how far we can get it to go. Let's try and do another one. Let's try again. Right. Three, two, one. Oh, that's a bit better, isn't it? Oh, lovely. It's going to land on someone. >> Yay. [applause] Okay, probably the last one. We'll see. Let's go to the other side of the room. Let's go this way. Uh, three, two, one. Oh, I'm sorry. I wasn't aiming at you. Never mind. These things happen. Try one more. We'll try one more. It's going to let me do one more. All right. Three. Let's go that way. Three, two, one. Oh, no. Not not happy that time. No, I've not got enough in that. That is That is the end of that. We'll do a round of applause. Thank you very much. >> [applause] >> Okay, my smoke machine says no. My smoke machine had enough. But um that's that's fine because what I've got uh is even better smoke rings for you uh from Mount Etnner. So this is a couple of years ago um in Sicily um Italy. Uh Mount Etnner was blowing smoke rings um and some tourists took some videos of it. This is footage from the BBC. They are just they blow my mind. They're just huge. Much more impressive than my smoke rings. Really very cool. It's lovely, isn't it? That's the right noise. You can come to all my talks, whoever that is. That is nice, isn't it? There we go. Um, so they're out there in the real world. Uh, not just happening here. This is what I say to young people sometimes. not just happening in your school or in your classroom, but they're out there in the real world. Um, and so, so volcanoes blowing smoke rings for the same idea. You've got like a force that's pushing smoke up towards the eruption obviously um towards an aperture at the top which which makes um the smoke ring. Um, apparently dolphins can blow smoke um not smoke rings, sorry, air rings. Dolphins can blow air rings. Um, and apparently they don't do it for any reason. There's no biological reason. They just do it for fun. Uh, which I just think means dolphins are amazing. They must be the most intelligent mathematical animals. They just play with them. There are videos on YouTube you can go and find um divers for the same reason divers can blow air rings as well um when they go down into the water blowing air through their mouth which is the hole. Um, so there's there's lots of other places that you can see this. Um, it is it's a type of vortex, right? So you might have heard the word vortex before. So any any fluid, so any gas or liquid that has circular motion um is a is a vortex. Um, and this is the toidal, if you want the fancy name, tooidal vortex, taurus shaped one. Um, different type of vortex, tornado, very different. Um, circular motion, but circles on top of each other, I guess. Circles around a line, right? That kind of thing. Um, a linear vortex. That's it. That's its name. Um, and it's a very different shape. Not circles around a circle, but circles around a line. Different shape. So, different behavior. Behaves very differently. Um, it's, you know, it's it's very destructive. It's not stable at all. Um, and, uh, and, um, you can do that in a water bottle as well. So, you can whiz your water bottle around and you can get, you can see the kind of tornado shape. Um, I am hoping we've got I've actually, this is unbelievable, but I'm I've finished with about four minutes to spare, which just is, you know, this doesn't happen, right? we can uh we can get excited about that. Um so what I'll do actually I'll use some of my time to show you a link. So I'm going to show you this link which you can go to um to find more out about this. So at this link ww.think-maths um that's my website.co.uk/smoke. Um that's quite easy to remember, isn't it? Think-maths.co.uk. Um then at that link there's lots of other bits that you can look at. So there's some videos um from numberfile from somebody else talking um about the maths of maps. Um and we talked a little bit briefly about um how the geometry of a flat surface is very different um from the geometry um of of the sphere. Um and uh so kind of linked to that is is the idea that every flat map that you ever see is wrong. Right? So every flat map you ever look at will have some sort of distortion. Um and so it's mathematically been been proven we can't perfectly make a flat map because of the difference of the geometry between flat flat surface and surface of the globe. Um and so for example, the Maka map, that's probably the one you most commonly see in a geography classroom or so on. Um is probably the most famous one. Um its distortion is its directions are correct, right? Things are in the right direction. Um but the sizes of land masses are distorted and it distort it makes the the land masses towards the poles look much bigger than they should be, which makes Greenland look much bigger than it should. Um if it was the real size, I wonder if Trump would take less interest in it. I don't know. Um, and it makes Africa look smaller than it should because it's at the equator. Um, so that's probably the most famous map, but there's loads of other types of maps that have have different distortions. And the maths of maps is just I absolutely love it. It's so interesting. So, there's some really interesting videos um you can go and look at if that interests you. Um, there's also there's the worksheet instruction sheet kind of thing um for Mobius loops, for the ones I've shown you, and other things that you can do with the Mobius loop if you want to go and try that with somebody. Um, that's on that link as well. And some maybe utilities. there's some utilities puzzles um as well that you can download and have a go at. Um so do go to that link if you would like. I think otherwise all I have to say is I'm hoping that you have enjoyed this session. Thank you so much for coming. Um it's lovely to be here um and I will go to I don't know where the Q&A tent is. I'm going to hope someone someone will show me and I know I will be at the Q&A tent um in in a couple of minutes. Um so thank you very much for listening. Hopefully I'll see you there. Um thank you very much. [applause]