 Cymru. Cymru, wrth gwrs. Felly, dwi'n peth sydd y gallu. Fyddechrau. Mae'n fath gwaith yma yn dda. Felly, ddim fath o'r dyfanc. Mae hynny yn gweithio gwneud mor fydd y byddai. Byddai ei wneud yn y begyn nhw. Efallai bod ydych yn gofyn fyddwch. Mae'n yn iawn cael ei fath ar y cyfaint yn y gweithiwn. Felly, yng Nghyru? Felly, ychydig yn gweithio ar y bêl i'r brif? Ond ydych yn gweithio ar hyn yn gwneud. Yes, my name's Katie and I am a mathematician and the title of my talk is indeed Katie Seckles does some maths. This is a consequence of being asked what my talk was going to be about a long time before I'd even thought about that. So I thought I would just give them something to work with. But essentially to kind of introduce you to me, I am a mathematician, which I guess means that I studied maths at school as some of the audience are still currently doing. I did maths at university and when I finished uni I decided I still hadn't had enough maths so I carried on. I did a little bit of research into various bits of maths and now a large part of my job is to talk about maths in various different contexts. So I go into schools, I do things at science festivals, I come to things like this apparently. I do stand-up comedy in night clubs, I talk about maths on YouTube, I talk about maths on the radio. Basically anywhere that people will allow me to continue talking about maths and not tell me to shut up is where you will find me talking about maths. So I brought along some bits of maths that I've been playing around with recently that I hope you will find interesting. And I want to show you a few different things. If anyone's worried that this is going to be serious maths, I am aware that it is Sunday afternoon. So none of this is in any way particularly technical or challenging, but just stuff that I think is quite interesting. Maybe if you haven't seen it before you may also pick up some useful life skills that you can take away and use in daily life genuinely. You know people have seen this and gone, that's great, I'm doing that from now on. So you know, hopefully. And yeah, so anyone who's just joined I'll be doing stuff on the table at the front. So if you want to come any nearer you're very welcome to do that, but we'll also put it up on the screen. Fantastic people running forwards, excellent. So the first thing I wanted to show, I've got basically two things I wanted to show you. The first one is a funny story really because as I mentioned I do talk about maths on YouTube very occasionally. So I've done a couple of videos for a channel called Numberphile which is a kind of maths YouTube channel which I recommend very much. Have you not seen any of them? I'm in about four of the videos, but they've done kind of several hundred videos and they're very, very popular. But I also have my own YouTube channel on which I have done three proper videos basically. One of them is a response video to someone else, but three of them are actually me doing a video about maths. And that's mainly because I do so many other things that I never really have time to sit down and actually make a video of my own. But one of them which went up last November just before kind of the Christmas rush. In fact it was near the start of December about Christmas related things. For some reason just went nuts and it's got nearly half a million views which is a lot more than I was expecting. And it was kind of in some of the newspapers like people were tweeting it around. A few of the media outlets actually covered it as a story and I was like what I just did a thing. I just made a little silly video and essentially what I'd spotted was a couple of interesting things that happen when you wrap. Presence for Christmas because I'd started to do a bit my Christmas wrapping and I spotted some really nice little things that happened. So I made a video about it and it just went mad and hopefully I'll show you some of these things. Hopefully you will find some of these interesting and or useful. But they're kind of fairly straightforward things that I'm surprised no one else had noticed. But anyway, stick that in there. So I've got a couple of clips from the, there we go it's over there. I've got a couple of clips from the video. So it was looking at kind of when you wrap a cuboid or any kind of regular shaped present you will find the standard way of doing it. Yes that is my Christmas jumper is to kind of wrap it round like that into a tube and you put a bit of tape on that bit. And then you can do this thing where you fold the ends in. So you fold them down and you fold the sides and you bring that up and you end up with that kind of wrapped parcel shape. And that's something that if you can master that you can basically wrap any cuboid which is fantastic. But I spotted a couple of things about this that you can actually do to make this kind of more satisfying, more mathematically nice. So if you can switch to the camera on the table. Is it going to work? One of the things I spotted was that if you're wrapping something which is a square on the end. So the cross section of the end of it is like a square. So this is just any old box of chocolates whatever other square chocolates are available. So that's like it's a square on the end. It's not actually exactly a square but it's near enough. So if you're doing this. Is that the right? Oh it's that way. I was going to say I cut this to exactly the right size. Yes it's that way around. So if you are doing this and you wrap kind of the tube tube ways style normally like that. Precut some salatate. This is blue Peter right. So that if you make the leftover bit of paper at the end. So the kind of the distance between the end of the thing and the end of the paper. If you make that half the height of the square. So it's exactly halfway up when you fold it in. Then you actually get a really satisfying shape on the end because you fold it down like that. And it's halfway. You fold these in and they come exactly to the middle as well. And then the bottom bit is exactly a triangle like that. And you fold that up and you get like a perfect cross on the end. Because if you have it any longer than that. Then you end up with loads of extra paper and it's a bit of a mess. But if you're much better at wrapping presents while on stage than me. You can see you get like a really nice cross shape on the end. So if you can flip back to the slides. I've got a video of this just in case that was more difficult than I anticipated to do while on stage. Here we go. So no not that one we've done that one. The next one. Oh not that one. No that one either. Oh maybe that one. Yeah go on then let's have that one. We've seen this come on. This is what happens when you make slides in a field. That is literally the previous video. And then does it just carry on? Did I just crop it badly? Yes I did. That's what happened. Okay. So that's a square end. It's square. Yeah. And you go halfway up. I've got a bit of an annotation there just in case you're not sure what I'm talking about. And if you now do that it's much easier if you can fast forward yourself. I've not yet mastered fast forwarding myself in real life. But you can see on there you pretty much get exactly that sort of beautiful cross shape. Right and this was the first thing that I noticed about this. This kind of set me off thinking about this because it gets better. Can we switch back to the camera? So if you've got a different shape. So this is I'm going to say this is one of the many triangular prism shaped chocolate bars that are available on the market. So if that's that's there on the camera brand name anyway. So that is actually even nicer because if you get your pre cut exactly the right size bit of paper this time instead of being halfway up the side. If you cut this so that the amount of paper left at the end is the same as the height of the triangle. So the full height of that triangle there is the length of the paper that you've got. I mean I couldn't believe how satisfying this was when I first did it. But you literally and hopefully you can see this if you fold that one in there and then you fold that one in you just get exactly the triangle. There's just the the the actual triangle is left at the end and then you just fold that up and it covers the whole end of the thing. Yeah, yeah. So if we if we again switch back to my slide so we can see that in less inept form here we go. So that's this one do it do it past me. Okay so that's yeah that's the thing and then if you fold the ends then that is just the triangle and it just covers it exactly. And it will be amazing. It's good isn't it? It's pretty good and it's just like it's just a thing about triangles. You know that's just how this this method of wrapping works. Anyway so these were sort of a few things that I put in my video but the one thing that kind of really inspired the video the kind of main exciting thing that I wanted to share with people was a method that I found in a couple of other YouTube videos online which I think some people have referred to as the Japanese wrapping method. But it's kind of it just it's just a way of wrapping a present who knows who came up with it. But it's it's really useful if you're wrapping something that's quite square and quite flat. I'm going with them sticking with the chocolate theme so I've got some cabri's milk tray which is quite square and quite flat also works with matchmakers chess. Anything that's square or rectangular and quite flat and it's actually just it's like it uses less paper or slightly less paper and it's just immensely satisfying. So what you do is you take a square piece of paper right and you want the size of this square. You can calculate it from this box so it's the length of the diagonal. That's a bit of a bit of a curveball for you if you weren't expecting that the length of the diagonal of the box. Plus one and a half times the height of the box so the kind of the depth of the thickness of it. So one and a half of that plus that diagonal there from corner to corner. And if you measure that you get that bit there and then a bit more for the height in the one and a half of the height. You can then cut a square that size. You stick that in the middle but at 45 degrees some of you might anticipate what's going to happen here. But you can literally fold up those. You can tuck those bits in to make that nice and neat. You can fold up that bit there. It's a lot easier if you've got more hands. That's all I'm saying. And then that bit folds in there and if you've cut this to exactly the right size, which I think I haven't but it's all good. That will exactly cover the present. So if you're slightly more generous than I am with paper, you can now stick that down with one bit of tape. Correct. Or if you're feeling particularly jazzy, just a bow, just a sticky bow. Just use that to stick it down. No tape at all. So that in the middle there. And that is now wrapped. Come on. I'm on stage. Can't you see all the people? That, if you make sure those bits are tucked inside and not sticking out like that, that is now wrapped. It uses one square bit of paper. I did actually measure the area of the bit of paper. It's not significantly less area-wise than you would use otherwise. But it's nice, right? This is much nicer. Assuming you do that right and it's not a bit wonky, Japanese wrapping method, apparently. So, yeah. It's pretty good, isn't it? Just out of interest, is it anyone's birthday today? Yes. That is an amazing coincidence. Do you know what the probability of that is? It's quite small. Anyway, come and see me afterwards. We've got three of our presents there. I'm going to show you. And I have another kind of thing. In fact, follow on from that story, because I say it was picked up by the media. I did this YouTube video and it just went mad. It was picked up by the media and I got a call from the Discovery Channel Canada. Genuinely, they were like, yeah, we do a show called The Daily Planet. It's a bit like Tomorrow's World, but now I was like, okay. And she was like, we just do like two-minute bits about people around the world who are doing interesting things with science. Would you like to do a bit about your Christmas wrapping stuff? And I was like, yeah, you're in Canada though, right? And she was like, yeah, we'll send a guy around. And literally a guy just turned up. He was from Chatterton. He wasn't from Canada. But he lives locally and does like, it's a cameraman thing. But he did the filming. He literally just turned up to my house and filmed me wrapping Christmas presents for the Discovery Channel in Canada. And this was a little time-lapse video that he did, which was terrifying. And they literally just did it in my flat with all my stuff in the background. You can see how many unfiled paperwork I've got there. And just all my random math stuff on the shelf. But he literally did a two-minute bit about me. And I had to say, because it's like a TV thing in America, Canada, they were like, can you do like a little intro bit where you're like, yeah, and you've got loads of stuff in your arms and you say what you're going to do. And I had to say, with these tips, people will think you've paid for model wrapping. And I was like, I don't know what that means. Well, I'll say it. Anyway, that's how my life is going anyway. So I've been on the Discovery Channel in Canada. But I'm not allowed to show you the actual clip. That was just a thing that he tweeted me because he was showing off his fancy time-lapse camera. But the actual clip went out in Canada. So anyway, this is another thing that I've recently been playing around with. And this is just one of my favourite pieces of maths. It's actually a piece of maths that's been proved. There's a paper about it. The way this started for me was I had a square. And I'm hoping you can all see that there is indeed a square on this piece of paper. And for unrelated work reasons, I had to cut out the square from the piece of paper. But I don't mean just cut out so that I've got a square. I mean I wanted a square hole. And I wanted to keep the square. So it was quite a complicated request. And I realised that if I wanted to do this, I could make my life easier by folding the piece of paper in half. There we go. So I can line up the sides of the square. And now instead of having to cut round, instead of having to jab a hole in it somewhere or do something untidy, I can just cut those three lines. And I was just about to get my scissors and do this. And I was like, wait, wait, wait. I'm a mathematician. Mathematicians are much lazier than that. So I'm not going to cut three lines when I could cut fewer than three lines, basically. So I was like, OK, I'm going to fold this again. I'm going to fold it in half that way. And now that will give me two cuts much easier, easier than three. But no, no. I'm going to get this as efficient as possible. I'm going to get this down to one cut. And some of you might be ahead of me here, but there is another fold I can do which will make this into one cut. I really apologise to anyone who's behind that pillar. If you want to move, just move. Like there's plenty of space. There's loads of space over here for some reason. Everyone came in and went pillar, me. Yeah, I'm going to sit behind that. Anyway, so this is now two cuts. I can make this better. I can do a diagonal fold. So this diagonal fold. Don't worry, it's not all this slow. I will pace it up a bit in a minute. That is now one cut. We'll cut out the whole square. Right? So if I cut that there, unfold this drama and I get a square. Yeah? Yeah? So genuinely, not the first time I've had a round of applause for a square on stage in various different contexts. I quite often go, a square! And everyone starts applauding. It's my job. So that was the thing that happened to me. And I was like, this is great. Save myself hours of cutting there just for this one square that I had to cut out. And I was talking to some friends about this down the pub, which is where the best maths happens. I was like, this is great. Save myself hours of cutting there just for this one square that I had to cut out. Which is where the best maths happens. And someone who I was trying to said, isn't there a theorem about this? Right? So a theorem in maths is kind of a fact that someone has proved that everyone can use that it's just out there for anyone to play with. And the theorem that they were talking about was a thing called the fold and cut theorem. Right? Because mathematicians name things like they are. They don't mess around. It's the fold and cut theorem. And it actually says, because what I was wondering was, I can do a square. Square is easy. Are there any other shapes I can do? I'm actually just going to move all of this stuff over here. I don't need that. So I can do a square. Are there any other shapes I can do? I started digging into it, looked at this theorem and there's a nice little story associated with this. So back in the past in 1777 I think it's quite a nice easy number to remember. They did a thing called America and having done America they were like, okay, we need a flag and we quite like stars. Let's just put all the stars on it. They put loads and loads of stars on it and in doing this they found that they needed to make a load of stars and they were like, oh, that's quite hard to cut out, guys. That's not an easy shape to get right. But luckily they found a seamstress called Betsy Ross and she was famous for having been the seamstress of the founding father team. I guess. I don't know if she was one of the founding fathers but she was around and apparently she knew a bit of maths because what she could do was take a bit of fabric and fold it up in just the right way so that if you make one cut tension, come on you get a perfect five point and start. And starshaped hole. But they were less excited about that. I'm excited about that. You've literally just cut along the edges of the shape. It's just amazing. So that's a little trick that apparently she knew on the basis of that got the job of making all the flags for the whole of the USA forever which was pretty lucrative, I guess. They kept adding more stars as well. They were like, oh, we've done another stake and you make a new flag. Yes, keep going, keep making the stars. So this was like a thing. Apparently Harry Houdini used to do this in his magic show. It's a really nice thing. And it turns out the folding cut theorem says that if you have any shape this is more dramatic now so I'm coming closer to the mic. If you have any shape whose edges are all straight lines even if it's got more than one bit to it even if it's got a hole in it any shape at all you can cut it out with one cut. One straight cut will cut out any shape called the piece of paper up first. And this is amazing and it's proved there's a team of mathematicians who've proved this they've got algorithms for generating folding patterns for different shapes and they've done a paper it's literally called folding and cutting paper the paper it's superb, it's a great read and they've got a little introduction at the start actually sorry, can I get a volunteer you don't need to get up or do anything but could you put your hand up if you have four letters in your name there's one right near the back what's your name for me good voice, I heard that Adam Adam Adam not Alan or anything that sounds like Adam that's also got four letters In the front of this paper they've got this little section where they explain the sort of history of this problem and they've got the little story about Betsy Ross and the star and they mention that Harry Houdini did this and one of the other things that they mention in this paper is that there was someone who could allegedly cut out any letter of the alphabet with one cut and I read that, I thought that's lovely I'm going to do that and I had a look around and I couldn't really see any reference for this or any information about this but what I thought was I'll just work them out I'll just do it, I'll just get a bit of paper fold it up, see if I can figure out how to do any letter of the alphabet and it took a while I'm going to say it took me a couple of months to actually get all of the shapes down some of them are easier than others I'm going to say I especially without the things on the top and bottom, pretty easy S is horrible thanks Adam for not having an S that is much appreciated of you but yeah you can work these out and it's actually quite a nice little puzzle so if you're into puzzles at all and you kind of want to challenge yourself to do something interesting it's a nice little puzzle to do I'm just going to try and remember how I don't mess this one up wait wait wait it's been a while since I've done this so go on then that's not going to work but never mind so that one's there you might have guessed what I'm doing here actually because I've learned how to do this on the stage and to a large extent while still talking but it's quite fun to sort of try and work them out start with simple shapes start doing squares and triangles and things and build your way up and eventually you can do them all and you can in theory do any shape at all so one time I actually did on stage a full life size paper cut out of myself with one cut which was amazing I used a paper tablecloth and I brought it on pre-folded because I'm not a masochist but I kind of had this thing folded up I cut one massive straight cut across the thing and folded it up and it was the right size as well because I literally lay down and drew around myself just for work so that was great and I've now folded four bits of paper that isn't going to work but it's okay so I'm going to cut these with one cut so that one there has one straight cut like that that one oh god that probably might work we'll see there are two bits, that's the middle that's the outside so that's more hopeful that one there and I'm now going to unfold these one at a time and if I have correctly made the letters of the word Adam then you may if you wish go completely wild with applause and I will say thank you very much and go if that's alright with you guys should we do this? are we up for this? I'm much warmer out there so you're better off in here but I'm afraid I've run out of things to talk about so I'm going to finish by unfolding an A wait wait it's going to get like you've got to ramp it up so don't start to right not confident about this at all but oh it's okay you can come and grab this after as well Adam it's great it's like a little present also if it is your birthday genuinely these have completely melted so feel free to take I have no use for them if you've got a straw with you you're all still up for grabs that's that's less impressive because you know I can already do that but I appreciate the applause anyway and to finish here we go