A Problem Squared - 009 = Big Statues and Big Stack Chews

Episode Date: July 31, 2020

- Could pennies make a girlfriend for the Statue of Liberty? - What's the optimum burger size for your mouth? - Where is Matt's topography video? Here's Bec's burger video analysis: https://www.youtube.com/watch?v=AAc2ukZVtdk And for Bec's 5KTS t-shirt, head here: www.bechillcomedian.com/5kts/square

Welcome to A Problem Squared. It's the British Bake Off of podcasts which try to solve problems. As in, there's nothing else quite like it, and that's not necessarily a good thing. I'm Matt Parker, roughly equivalent to the contestant on british bake off who always takes the exact details of the recipe too seriously and i'm joined by the no fielding of people who aren't no fielding beck hill yeah that's an intro to a podcast yeah it is matt parker is the one who goes to the effort of writing a proper intro for a podcast and i'm beck hill who wings it hey that's kind of you thought we should up our game you know there you go into an intro to a podcast i've been going through all my old tweets and i

actually found my tweets when they announced no Fielding as the... Really? Yeah and one of my ones that went quite well was saying I can't wait till the new British Bake Off purely just to see Noel Fielding tell someone that their flan contains too many memories from another realm. Why am I not surprised you had a Noel Fielding flan story? But have you been back? You good? Flan story. But have you been back? You good? I'm good.

I'm good. Actually, something I haven't announced or told anyone because by the time this goes out, then listeners might know, I have been announced as the ambassador for the UK Craft Council. No. Yeah, yeah. And so they're doing a new campaign over summer. They're trying to send out 10,000 arts and crafts packs to kids who wouldn't necessarily have access to arts and crafts materials so that they can get creative during summer holidays.

That's amazing. I had no idea we had a craft council. Yeah. And you know what? I'm glad too because now i get to go to those parties where they all have pyramids of ferrero rocher that's why i said yes to it makes sense so i'm mildly distracted because the um way you calculate the number of such ferrero rochers in that shape stack is an interesting maths problem in its own right. Do you have references that I can refer to for that? So it's a square-based pyramid of circular things.

How do you know this? It's literally what I do. I didn't even know it was a square-based pyramid. I thought it was done like a circle. No, that's how you want to stack. Unless I've misremembered the ads, and if they've done it a different way, they've done it wrong.

I can say that. I'm already sensing what one of our problems for the next episode is going to be. And 4,900 is the only number of Ferrero Rochers that you could arrange in both one of those pyramids or lay them out in a giant square shaped box like what they would originally come in. So there you go. Fact. Which brings me to what I've been up to.

Did I mention I won an award? That's been my big achievement. What sort of award though? For mass communication as just demonstrated. Right. So I got the Christopher Zeman medal. Did they pay you in Ferrero Rocher then? I hope so.

But it's a physical medal, which is very exciting. And I'm only bringing this up because in a previous introduction, we referred to this podcast as not yet award winning. And given I got an award for a very nebulous just communicating mathematics and i've been known to chat about some maths in this podcast yeah i think in a very real sense the award is partly for a problem squared and so i think we are now partially award winning podcast a problem squared yeah 50 award-winning podcast yeah we get there well you know unless unless we can somehow jam in my best kids show at leicester comedy festival 2019 somehow to be relevant in this podcast i think we've got enough bits of awards that it

counts as as um becomes a whole a whole. A whole award. A whole award. Yeah. And in this episode of our tenuously award-winning podcast, I will be solving the problem of how many pennies make a statue. I'll be looking at the perfect height of getting a burger into the average mouth. And we'll have an update on my topography land area video. That is to say, an apology with all the interesting reasons on why it took me so long. At Andrew underscore

Taylor has tweeted a problem to us, but they've also quote tweeted someone else as part of the problem. They've quote tweeted at dumb bass online, or dumb bass like the fish. One of the bees is silent and one's not i guess yeah there's two bees i'm i'm not the one being a dumb bass dumb bass and uh they tweeted saying

we need to melt down all the pennies and make the statue of liberty a girlfriend so quite a funny joke good tweet good tweet got about 30 000 retweets, so yeah, it did very well. But Andrew's quoted it and sent it to us saying, would the resulting girlfriend be far too big, far too small, or sort of about right? Great point. I can't believe no one, those other 30,000 people retweeting it, they must have thought about the same problem surely. I mean, I'm just, look, I'm looking at the replies to the initial joke now. Oh yeah, what do they got? Anything good?

Someone says, tell me why did I read it as penises? Okay, yep. I'm guessing they meant as pennies and not, you know, statues or something. And they're just getting mistaken. Someone said she has a long distance girlfriend in France. And they've shown a similar statue in France. Ah. No one looking at the realities of this joke.

Well, have I got some realities in a spreadsheet for them. So, first of all, I mean, I agree with all the aspects of the premise of this problem. So, yes, a statue, girlfriend, Statue of Liberty. Great idea. I'm on board. But also getting rid of pennies, definitely on board. I think the one cent coins in the US and pennies, one and two pieces over here in the UK, we don't need them. We don't need them.

And I remember when they got rid of one and two cent coins in australia and we have not looked back no one's like i miss my cents no you don't we don't need them we don't need them not in a monetary way yeah and everyone's like oh but how do you like you can't pay for things exactly and you think i would be exactly the person who'd be upset at the fact that you cannot precisely pay for things in cash anymore. I really liked it because you can still precisely pay for things if you use a card or an electronic payment, but if you're paying cash, it's just rounded to the nearest five cents. And so what I would do is if I thought it would round down in my favor, pay in cash if i think it would round up not in my favor i'd pay on card so you wouldn't have the rounding and so you could save literally tens of cents a year

wow by strategically choosing how you pay and which way it rounds didn't they make catch me if i can based on that story that caliber yeah of uh yeah hijinks and who's your tom hanks there's someone out there going the rounding bandit is at it again it's like office space but i mean really really really it's a bit like the plot of Superman 2. So, oh, I've just had our producer John in my ear saying, because they are an expert on terrible films, it was Superman 3 that the penny scam was in. To be fair, I haven't seen the old Superman films, so I wasn't actually referring to that plot.

I was referring to the quote from office space where they say it's just like superman n and so i was trying to remember the quote from office space i just go i've got producer john on my ear again apparently superman n is accurate enough also for anyone listening um ghostbusters is the one with the statue of liberty yes correct sorry i've just had producer john in my ear oh really really just clarified that it's was it ghostbusters and got it right so i think they should get rid of the pennies one cent coins, in the US. However, there are currently a lot of them in circulation. There are, according to the numbers I found, 130 billion pennies in circulation in the US as we speak. And they last on average 25 years.

That's a lot of pennies that's almost a billion dollars who knows how much they're worth but they're out there and they're since 1982 they're largely not copper anymore so before 82 immediately, people love copper. And from 1962 to 82, they were 95% copper with 5% zinc mixed in, just to make them, I guess, a bit hardier. And they weighed just over three grams each. In 82, they swapped it around. They're like 97.5% zinc and just 2.5% copper. That's a lot of zinc. A a lot of zinc and so you don't

get much copper and i think the reason that people thought melt the pennies down gives us a statue of liberty is the statue of liberty is made of copper is that yeah well so the statue of liberty was made by france and it's got like an iron structure inside. Skeleton. A skeleton. Thank you. Slow down with the technical language. And over that is draped plates of copper and they're less thick than two pennies put together

in the States. That's very thin. It's got to be thin. So there's actually, comparatively speaking, not that much copper in the Statue of Liberty because it's just this tiny layer on the outside. So there's not a lot of copper in it. In terms of the actual numbers, if you work out the amount of copper in a penny, the number of pennies in circulation, and the amount of copper in the Statue of Liberty,

which is not a straightforward number. No one's entirely sure different people argue about it i've gone with it's a hundred tons of copper total in the statue of liberty you could if you melted down all the pennies just got the copper make 81 and a quarter statues of liberty or similar statues of a similar size. Wow. Or you could make one statue which was nine times as big. That's a big girlfriend. Yeah, I don't want to be judgmental.

I don't know what scale of girlfriend the Statue of Liberty would like. And nine times is bigger than I expected because I thought that when you, because when you scale something, the volume goes up as the cube of how much bigger it is. But actually, it's only the surface area of the statue which counts because the thickness of the panels wouldn't increase. And so nine is actually a pretty big increase. Like that's a lot more statue for your money. I tell you what though they would really benefit from listening to our last episode where they could work out how to

get different height counters for their kitchen yeah that you'd see the relationship could work yeah you know if if they want to make it work there's engineering solutions for any problem they may come across yeah but then i was like couple of things that are unsatisfying about this because you still need the inside skeleton of iron. And I looked up like if you could use the zinc, the leftover zinc from the pennies. And zinc is not a structural material. Can I also ask, Matt? Yeah.

You said that before it was 82 82 they were a lot of copper and then after 82 they were less copper have you taken that into account because it means all the pennies that were produced before 82 have more and then since then have less i have not because i looked up and the u.s mint assumes pennies circulate for 25 years on average. And because it's been coming up on 40 years since they switched over, I've decided there's a negligible number still in circulation with loads of copper. I could be wrong. The mint doesn't give a standard deviation.

Just the ones that are out of circulation. Maybe they're already a statue. Well, exactly. Where do they go? They've got to go somewhere. Are they're already a statue. Well, exactly. Where do they go? They've got to go somewhere. Are they lost? A lot of them are destroyed. Do their banks, I don't know, do banks take them out of circulation if they're too worn out?

I mean, some coins last a very long time. Before they switched to decimal currency in the UK, there were coins still in circulation, which were hundreds of years old. Just incredible. However, I looked up and because the population is increasing and the amount of currency required is also increasing, the Mint currently makes 13 billion new pennies every year. Oh, that's a lot of pennies. They are constantly putting them out. So my actual plan is what America should do is stop making pennies. It's ridiculous. It's gone on too long.

They got rid of, they had like a fraction of a penny coin. They got rid of that in the 1800s. It's time they got rid of the penny as well. But when they get rid of it, because maybe the mint has already pre-ordered a lot of metal, maybe people's jobs would take time to re-skill and re-tool for making other coins at the mint. When you stop making pennies, the pennies you would have made for just the next year, the next 13 billion pennies, you take all of that metal, the copper, the zinc and everything, and you make a solid statue, which is the same composition as a penny. And that statue, I did the calculations on all the volumes, will be within 10% of the size of the Statue of Liberty.

What? So it would be like 1.1 times as big. So it's 10% off. That's as big. So it's 10% off. That's all right. She's just a bit taller. Might be a bit taller. Might be a bit smaller. Maybe she's packing a bit of boom, boom, yeah.

Maybe she's got a bit of junk in the trunk. Exactly. Who knows what kind of statue it's going to be. It'll be roughly to scale with the original Statue of Liberty. And I double checkedchecked this long-distance girlfriend story in case they were already in a relationship with one in France. And there is a quarter-scale Statue of Liberty in France. It's on an island in the Seine.

However, I've seen it referred to as a sibling statue. Oh, like a little sister. Oh, like a little sister. Yeah, like a little sister. So I don't think it's a romantic relationship. We want a statue that's incense, not incest. So I figure... Thank you. Thank you.

That's my one pun for the show. So I don't think that's a big problem. We can make a girlfriend for the Statue of Liberty, not with all the pennies in circulation, just the ones that would have been used in one year when we stop making pennies. It's ridiculous, people. Stop it.

Or we could just like stick them to the Statue of Liberty, make her a nice little jacket. There you go. Like a sequined jacket. That's what it would be like. Oh, yeah. There we go. Showtime. Yeah. Problem like. Oh, yeah. There we go. Showtime.

Yeah. There you are. Problem solved. Ding. Yes. We have a problem sent in on Twitter by at Burgermeister MB. Yo, I love burgers. I hope I'm giving this an honest reading.

But people keep making them. That's an M with an apostrophe E-M. Too tall and I can't fit them in my mouth. Question. For a standard human jaw, what is the upper limit of burger height such that you can bite through top to bottom in one chomp? That is a great problem. Beck. Oh, I love that.

I love that problem. And I jumped to it as soon as we got it. I was like, Bagsy, this one's mine. Yeah, you claimed, I hadn't even seen it and you'd claimed it. I claimed it immediately because I knew that answering this problem would require me to test eating a bunch of burgers. You were the person for the job, I'll be honest. test eating a bunch of burgers. You were the person for the job, I'll be honest. Yeah.

So the first thing I did to try and solve the problem is find out what the average jaw height is. Oh, like the average caliber of an open mouth. Yes. And basically it's somewhere between 35 and 55 millimeters. So basically it's the same as roughly three human fingers so there's a i i tweet i found a figure where it was explaining how wide the average human jaw can open and i tweeted it that you retweeted i did and it's basically if you were holding up three fingers in front of you and trying to line them up to fit in your mouth and i tweeted it uh to check if this was because

it fits in my mouth but no more i can't do any more than three fingers there's a little bit of wriggle room but not enough for a fourth finger because i saw your tweet yeah I did and I so what happened was I tweeted it saying you know is this true for you just to double check and yeah I want to fact check these things and I found out two things if you tweet about that one is it's an incredibly irresponsible time for me to tweet something that encourages people to put their fingers in their mouths yeah a little tone deaf there, if I'm being honest. Yeah, I had to suddenly put in another tweet just saying, please wash your hands before and after.

Before and after, yeah. Yeah, and use your own fingers, not someone else's. Shouldn't have to clarify that, but yep. So that was one thing. The second thing I realized, if you tweet about that, is you will be bombarded with photos that people will take of them with their hands in their mouths. Yeah, because I retweeted you, which I would have done anyway, because I want to encourage our research for solving problems, for a problem squared. But I saw your tweet and I was like, I've got to try that. And so I did.

I was amazed. It's like exactly three fingers. Yeah. And I assume the size, like your fingers scale their size with your jaw size. And it was such a perfect fit. I was like, oh, that's amazing. And I knew if I retweeted it, you'd get more hilarious photos of people putting three fingers in their mouth. Well, the thing is, if people didn't see this on Twitter who are listening to this now, they're definitely putting their hands in their mouths now.

Oh, yeah. Like someone, you're listening to this right now and you are either right now putting your hand in your mouth. Oh, it's worth it. Do it. Do it. Or you've just done it. It's amazing. Please wash your hands. The interesting thing is there were, I didn't count percentages because this wasn't part of the problem, but there were people who had four fingers. Wow.

No way I could do four. Some people could fit even more than four. Nah. I found out that Gavin, my husband, can do four. What? Quite easily. He's got a very, very big mouth. Wow.

I had no idea. I always thought I had the big mouth in our relationship. And then there were people who can just barely do two. Some people, it was due to various conditions. Other people, it was, I don't know, just the way they're born. There's no shame in any of it. You know, everyone's different. The interesting thing was amateur Saman, who is at Saman Biswa, who's a comedian, musical comedian, and most importantly, doctor. Yes, of the amateur transplants thing. That's right. Yeah, yeah. more than two fingers then and you go for surgery you need to let your surgeon know because it might

affect in terms of when the anesthetist it might affect getting the tube into your throat and everything so yeah yeah who knew potentially life-saving advice from encouraging people to put their fingers in their mouth yeah yeah well i, it's also part of first aid, isn't it? Probably balances out with the downsides of encouraging people. So I was able to confirm that. And yeah, for me, I've measured it. My jaw can open up to five centimeters, so 50 millimeters, which is, yeah, pretty much bang on what the average is. 50 millimeters, which is, yeah, pretty much bang on what the average is. And with that in mind, obviously the quick answer to this is that any burger that is more than three fingers is most likely going to be hard for the majority of people.

That's great. Some people might be fine, but also you've got all those people below that, which definitely won't be able to do it. So a burger should be roughly three fingers in height yeah because if you make a burger that matches the average half the people won't be able to eat it yeah you want to go average you want to get something that's accessible yeah so yeah but it sounds like the vast majority of people can do three fingers definitely two give or take yeah yeah so actually you know if you want to be really safe two fingers two fingers but um but on average about three three okay i wanted to check how that measured up against some major burger franchises your dedication to solving problems

for our listeners is just unparalleled i I'm so dedicated. I spent all of my Saturday ordering five, well, first of all, going through all of the most popular franchises that were offering delivery to my area. Yep. Because obviously it's still a bit tricky with lockdown. You're not going out. You're not going out. And searching their menus for either the tallest burger that they have or sort of the most, you know, some of them had like a special which might not come back. Right. So I thought I'll go for the tallest common burger that they have that's on their menu all the time. When you were doing this.

Yeah. You told me you were going to do it and you're like, oh, I'll send you some updates. And then I heard nothing yeah and i thought it's either gone really badly or it's gone really well and you're like i don't want to ruin the surprise for matt well first of all i didn't eat anything that day until i got around to filming because i knew i was going to be eating five burgers and i figured that i would have more space with an empty stomach. The problem is if you don't eat until late in the afternoon, you get grumpy. Hangry, I believe, is the technical medical phrase.

Yes. The other thing is I had to take photos and film because I turned it into a video as well, into a YouTube video, which will be out around the same time that this comes out as well so if you if you want to see visuals of this and we do head over to my YouTube channel um I had to film all the burgers and take photos of them at their various heights and measure them and everything which meant that I was starving and looking at five delicious burgers that were all getting more and more cold. And I didn't want to like reheat them in case it like changed their integrity or, you know, because then you might lose some of the water due to the heat.

And so then it might be smaller than it's supposed to be. So all the burgers I'm eating in that video, little behind the scenes for you. Stone cold. Delicious, but cold. You ate nothing but cold burgers. Yeah, so by the time that I got to a point that I thought I would be sending you updates,

I was indeed too hangry. Also, the delivery drivers, two of them arrived at the same time, so twice, so like four of them arrived. In pairs. So good. Especially when it was, two of them were very major competing burger joints

they those two arrived at the exact same time which was really funny they must have thought we were racing them yeah so yeah i did that the other interesting thing is it's one thing when you order something off a menu in the restaurant and you see the difference between how it arrives and how it looks on the menu now fast food joints you kind of expect a bit of that but from more of the gourmet franchises that i ordered from normally you'd sit in and you'd have you know they give you those steak knives and the burger comes with like a sort of a skewer through it a skewer holding it together and all the photos made them look so big and amazing and balanced. One of them had

very good packaging and you'll be able to tell which one from the video, but a lot of the others arrived quite squished. Right. Yeah. So their height was already compromised. It was compromised. Would you like to hear the measurements of them? I can't wait. I didn't want to ask, but I'm very excited. So burger number one. B1. Yeah. I'm going to do it in height order. Do you want to have a guess at what the least tall popular burger was? Is it like a Whopper from Burger King? It is. It's the, I got the double Whopper. Oh. Because I still wanted to see how high I could get them. You went all out. Yeah. And that is like still a common staple on the menu.

So the double whopper comes in at six centimetres high. Okay. The interesting thing about the double whopper, and you might want to write this down, Matt, because I forgot to take photos of the measurements, but I took the measurements. The double whopper was the largest in diameter. Good.

Because it was 12 centimetres. 12 centimetres in diameter. Yeah. Solid. Two to one ratio. Love it. Do you want to guess what the second, well, the fourth tallest? Did you get a chicken based one?

I did. Is that the one? Does that come in there? No. No. Well, it does come in, but it's not here. Because if for McDonald's, if you got the cheeseburger, that's shorter than getting like a Big Mac. Because the Big Mac is like a multi-tiered affair yeah yeah so i assume you got the big mac it was a big mac it's actually not as tall as you'd expect it the big mac is only seven centimeters tall now bearing in mind that my mouth is about

five centimeters wide so already the double whopper is supposed to be twice as big um your big mac seven centimeters tall 10 centimeters in diametercm. And do you want to have a guess at what the third tallest burger is? I've lost my confidence in burger guessing. It's a Zinger Stacker. Oh! KFC Zinger Stacker because it's two Zinger fillets on top of each other. And that's where you get your height from mainly because they're not sort of flat. They're sort of oddly shaped. That said, only 0.3cm taller than a Big Mac, 7.3cm. That's where you get your height from mainly because they're not sort of flat. Adds up, yeah. They're sort of oddly shaped. That said, only 0.3 centimeters taller than a Big Mac. 7.3 centimeters.

That one came in at. That's not much. And slightly, slightly slimmer at 9.5 centimeters in diameter. Got it. Then the next one was the Honest Burger, which, oh my goodness, in the photo looked so, so tall. So it's the Honest Burger and it was a vegan one. And that came in at 7.5 centimetres and 10 centimetres width. Barely, barely above.

And then the biggest burger by far was, it's not a major franchise, but that's because a lot of the other ones did not deliver to my place. So the most famous one I could find in terms of the amount of people ordering from it was Wicked Burger. They had a 10 centimeter high burger and 11 centimeters in diameter. That's outrageous. It was huge. Because I was just running those numbers. I'll put them in a spreadsheet as you gave them to me.

Up until then, the Whopper was the biggest by volume wow yep but it just got blown out of the water by wicked wow so yeah with the testing um the first round i did i didn't squish them at all obviously there's a little bit of give because you've actually got to grip the burger so you've got to allow for that i had a technique which was to hook the bottom of the burger over the lower teeth like fulcrum it in yep yep yeah yeah so tilt it in so the the whopper was fine was able to get one bite in that from top to bottom the big mac was fine top to bottom the zinger one that was where i started to struggle that um i barely got a bite i just managed to get from top to bottom with everything in it honest burger was where i got stuck i couldn't i just physically couldn't put it into my mouth and that meant that the wicked burger was definitely out of the game so that was where i sat with them. The next test was, okay, these burgers from the beginning

are too tall for my mouth, but what if I squish them? Yeah. Because we all like a good squish. Standard burger procedure. You press them down. Yeah. And so I did it just with my palm. I didn't sort of use a standardized squish because I did toy with putting a phone book or something on top of them.

But I don't know if you've seen the phone books these days. They're basically pamphlets. So that was out. Also, you know, don't normally carry a phone book to a burger restaurant. So I figured I'll just go with my palm and my body weight. Fair enough. And we'll see how we go. It's practical.

So the whopper, when squished, the Whopper comes to five centimeters. You'll lose a centimeter off of that. The Big Mac, you'll lose 1.5 centimeters. So it goes down to 5.5 centimeters tall. Yep. The KFC Zinger, I tell you what, that chicken, a lot less squishy. Chicken, pretty rigid. Yeah. Only lost 0.3 centimeters. So it was seven meter tall, the Zinger. I tell you what, that chicken, a lot less squishy. Chicken, pretty rigid, yeah.

Only lost 0.3 centimetres, so it was seven metre tall, the Zinger. Wow. Yep. Honest Burger only got 0.5 centimetres off, so that was seven centimetres in total. And the Wicked Burger, Wicked Burger, squished that down, lost a whole two centimetres. Whoa, down to eight. Went down to eight centimetres. Huh.

Yeah. It feels like all the burgers that weren't chicken or vegetarian, the standard burgers, all compressed to about 80% of their original height. I think that's a pretty standard amount of compression in a meat burger. So if people are planning a purchase, you can assume you'll get 20 of the height taken off with the palm press there you go how's our volume looking i've run the numbers and wicked burger still got the most volume and the whopper still coming in second wow but then because kfc and honest didn't have much compression they've overtaken oh actually honest has maintained its spot and kfc has overtaken mcdonald's for sheer volume so the big mac but you've not changed the amount of burger

and i is i'm curious to know possibly weighing them would have been interesting to see what the density of the burgers was however that's not really needed because the question just was can you fit it in your mouth not how much burger are you getting yeah that's true really needed because the question just was, can you fit it in your mouth? Not how much burger are you getting? Yeah, that's true. Yeah. We just like to give these details as a bit of an extra, don't we? Because we're professionals. If I was to give one detail as an extra, because when this problem came in, I was like, I'm genuinely interested because I get really annoyed when places serve burgers that are too tall.

Yeah. And that's partly for practical reasons and i say if you need a skewer to hold it in place i'm glad you brought that up earlier you've done something wrong in your burger planning the burger should have its own structural integrity it should not need scaffolding it should not need anything inedible to hold it together it's a load-bearing skewer yeah exactly i don It's a load-bearing skewer. Yeah, exactly. I don't need a load-bearing skewer or external supports. You can't cheat and give it, like, spread out on the plate.

And when you try to assemble it yourself, you're like, oh, this is too tall. They have not thought this through. The other reason it annoys me is it's the inefficient way to gain volume in your burger. Because if you make a burger twice as tall, you only get twice as much burger. If you make a burger twice as wide, not only does it stay easy to eat, but you get four times as much burger. It's far more efficient to make a burger wider than it is to make it taller. But for some reason, that's what burger places do. I can only assume there's some psychological thing where the way humans process size, we favor height over width.

But it just annoys me. It's so infuriating. Like filming with your phone, you should be going landscape instead of portrait. Exactly. Well, I tried it once I squished them down. And I managed to get a bite from top to bottom in every squish down burger until I took apart the Wicked Burger and realized I'd missed a level of onion rings that were hiding in the middle. So that's the only one I couldn't do in one bite. So Wicked Burger sounds like good for volume. You'll get a lot of burger, but you won't be able to eat it properly. Yeah. I'm glad you included

Wicked. So there was a representative of that kind of unnecessarily tall burger joint. Like the independent ones were just showing off, honestly. If you need a knife and fork. It's not a burger. That said, if you're making a wide burger, at what point is it a pizza? Okay, true. Okay, there is a ratio here somewhere. Also, I accept cutting a burger in half and then eating it. I'm okay with that.

Oh, get out. No, I'm single cut. That's not part of the burger eating. No, it's not a sandwich. It's part of the pressing it down. You also cut it in half. You eat it a half at a time. No, no.

Really? No. Oh. Wow. I didn't realize that in solving this problem, I would create a new one, which is how do I remain friends with you? Who's correct? Can you cut a burger in half?

Should you cut a burger in half? Tweet us at a problem squared. Speaking of tweets, we have basically solved this problem, but this is a weird thing. I don't know if anyone can solve it for us who's listening. So this tweet came in, as you said, Matt, from at Burgermeister MB. Yep. They didn't have a profile picture. They'd asked a burger-related question and their handle

was very burger-specific. So when I looked at their tweets and replies, which is, you know, normally where sometimes people won't do their own tweets but they'll use Twitter to communicate with companies and people and stuff. We're the only ones they tweeted. One reply was to us.

With that question. Yes. You went to go find this, Matt. Yes. And then what happened? So when I was about to read the question to you in this podcast recording, I was like, you know what? I also went, it's pretty funny.

It's a burger related name for this. I'll just double check I've not got that wrong. I went to load up the tweet and their account has been suspended so when you go to see this tweet it just says account suspended and then the cryptic twitter suspends accounts which violate the twitter rules now i'm just opening up the old Twitter rules here I'm doing a quick ctrl F find I'm typing in burger nothing no mentions of burgers in the Twitter rules

putting in mouth nah nothing so I don't know I don't think they were threatening violence against us I'm just flicking through all the horrible things people have been banned for oh my goodness I didn't report them

I did not report them maybe Big Burger got to them oh yeah you've blown this case wide open well whoever you were if you're out there at Burgermeister MB if you're out there let us know you're okay and know that we've solved this for you

start a new account different name don't be traceable just tweet ding and then disappear back into the night. Fight the good burger fight. So Matt, you might remember on the last episode of A Problem Squared. Yeah, I know where this is going. We had a problem about topography. Great problem.

In fact, can you remind us what the problem was? So, Phil Chapman sent in a question on Patreon, I think, saying, do countries include the terrain, the topography, the up and down of the landscape when they calculate their official land surface area values? And you partially answered it. Partially. And so I gave you a duh but no ing and you said that you were going to film a video about it for youtube yep and i said are you sure you want to say that it's only two weeks away

so matt how's that uh how's that video coming along it's coming along so i did not get it done in time for when the last podcast went out which a lot of people will obviously be aware of because they've been asking matt where is that video and the problem was i was originally thinking you know what it'd be kind of fun to just do a video in my room i I filmed it like a little studio at home, talk about what I covered, show some cool visuals, job done. However, I kept learning new things and I kept more solving the problem. At the same time, the scale of the video kept increasing. So it didn't get done in time and i know i'm potentially making the same mistake twice when i say i'll definitely have it out before this podcast goes out i swear surely surely i'll have it done when people are listening to this so it's dangerously close to being finished and as penance for making promises i couldn't keep

i can give an update on a better solution to the problem because i ignored some of the other bits so on the first bit i was able to confirm that the uk does not include terrain or topography when calculating the land area okay and that's that's because Dr. Laura Graham of the University of Birmingham, an academic, got in touch and offered to help me, which was much needed. And Laura normally researches how the structure of the physical environment impacts biodiversity and human well-being, which is important research. But it meant they already had geodata at their disposal and they had the know-how, which I did not,

to be able to do calculations on that data. And they were able to recalculate the flat area of the UK and show, if you look at the official figures, that the official figures do not include the terrain. So I've comprehensively answered the first part of the question. The last part of the question, we'll get back to the middle in a second, was how does it change the rankings?

And last time I was like, Switzerland? I can now say Switzerland because I can confirm if you include the terrain as Switzerland, it overtakes the Netherlands in the official world rankings of surface area i know it goes up it goes up maybe two it depends if denmark how much denmark goes up if you include its terrain

because initially it goes over the netherlands and denmark but i think denmark might regain its position once you factor in its terrain whereas the netherlands no way that's flat it's not going anywhere i mean how much land can they reclaim at short notice is what i'm saying not enough to retake its position from switzerland so that's great another bit done also i ignored this last time because i didn't think i could answer it and as part of the question phil said if they don't include the terrain do they assume it's perfectly flat or do they assume it's a perfectly smooth part of a sphere because obviously the the earth has curvature to it i don't know how to work that out and so i did some rough calculations and worked out that for a country like the UK, which is very small, it would only

change the value by like 0.1, maybe 0.2% tops if you factor in the curvature of the earth versus a flat footprint. So we don't bother. What is that in terms of, would you say that's like meters or are we talking like kilometers? Well, yeah yeah it's still kilometers because the uk is 240 ish thousand kilometers so 0.1 is 240 kilometers that's a lot still if you were going to give me 240 kilometers squared land square kilometers yep i'd be pretty happy with that good point good point but it's within the kind of precision of the other measurements and data like it's not compared to the ambiguity when we do the calculations on where the border actually is it's not massive is what i'm saying and that that's a maximum so i just assumed that the whole of the UK was like a disc roughly the size of the UK

and compared that to the cap on a sphere. So it's probably a bit less than that. Whereas for Australia, it's like one or two percent because it's so big. And that's millions of square kilometers. Wow. So that's like, what would that be like tens of thousands? Like it's a huge change. And also, Dr. Laura Graham was able to confirm that they were just using a flat footprint for the surface area for the UK.

They don't worry with the terrain. Whereas for Australia, I got in touch with Geoscience Australia again, legends, and they came back with an answer of sort of. So the data they use for where the borders are of all the states in Australia, because they do it state by state, they're on a projection of the earth that compensates for its curvature, a thing called a conic projection, which tries to preserve area. So they do compensate for the curvature of the earth. And they say the same thing. They do that to the level at which it matches the accuracy in the original data they were using. So the answer for the middle bit is yes.

If a country is big enough, they do assume it's a sphere. So now, when I had all this extra stuff I found out, and Laura had done all these extra calculations for me, the video got bigger and bigger. It also got more and more grand because I'm like, oh, I can't just film this in my studio. If I'm talking about the terrain of a country, i should be out walking around the terrain of the country and so i went out and filmed a bunch of stuff i may have bought a drone it got a little over the top

but that meant i also had to increase the production quality of everything else so i got in touch with phil and said hey Phil, could you record yourself asking the question? Because then I can drop that in the video. It looked really nice. And Phil happily did it. Laura very kindly recorded herself answering the questions for me and explaining what she did. Amazing. And Beck, as you know, I got in touch and said, I need a voice of Geoscience Australia to read out some highlights from the answers they sent.

Yeah. And you did an adequate job. I did a great job for something that contained zero punctuation. That's true. The punctuation was heavily implied. No, it was implied if you have context. Yeah. And understand the words that you're saying.

Good point, good point. So I put your reading and your complaining in the video. Good. Well, I'm glad you left the complaining in because so did I. Now, since then, I got in touch with Geoscience Australia again to get the information about if they include the curvature of the Earth. And they sent back their answer and I want to put it in the video which means I need more of the voice of Geoscience Australia so I've emailed it through have you got have you got the the bits you've got them there I do I have them here I'll put on my best Geoscience Australia voice okay good the area calculations are based on the equal area conic projection

that attempts to minimise the area distortion proportionately of a global map projection based on the Australia geoid. Since this particular projection minimises the distortion of area computations from spherical geometry to flat map, it is used as fit-for-purpose area calculation based on the resolution of the coastline data in the 100k. Geoscience Australia. I still have no idea what I just said. I want you to know that I have no idea what that was. Nailed it. That's excellent.

Ray. Job done. Ding. Oh no, no. You've just got a duh. Well, can I get the E, like the I? D. That's what you get so far, but you don't get the M. Thank you. To be continued. As always, thank you so much to listening to A Problem Squared. It's a huge amount of fun to do these podcasts, and this is currently episode 009, which means, episode 009, which means, Bec, we are three quarters of the way through our year of doing a Problem Squared.

Yeah. This is like a quarterly update. We've got a target, don't we, to be able to continue doing the podcast after a year? We do. And early on, we were way ahead of projections. We got very confident and we stopped telling people about Patreon. Yep, because we were like, we've got almost 50 Patreon supporters. We're going to hit, because our target was 100.

We're like, we're almost halfway there. And just looking at the current number, we are almost halfway there. I mean, from the other direction, We've now got 56 Patreon supporters. So thank you so much, all 56 of you. Yes. Our goal was to have 100 people who think this podcast is worth donating a bit of money for each month. And that means we have a system to keep doing this. So people already giving us money.

Thank you so much. By the way, we appreciate at the moment, if you're feeling financial pressures for whatever reason, it's a bit tough with the economy. It's fine if you've got to stop. Yeah. Don't be guilted into it. It's fine because all these other great people who are listening now thinking I could do that. They're going to step in. They'll take up the slack.

Don't worry. We got this. Enough of this. We can make this work. And if anyone's listening and you're like, I was never a supporter to start with and I'd love to be one, but this has been a tough old time.

The next best thing you can do, which is maybe arguably just as good, is tell people about it, share it, get other people to subscribe to us, give us a five-star review, anything you can. Because if we can get enough listeners, then there's still a way that we might be able to make this work. And an extra, extra, extra special thank you to the

I'm a Wizard level Patreon supporters, because we have an extra episode that goes out with this one each month. Episode is a strong word. Itty bitty bonus content yeah you get the behind the scenes of us warming up and getting ready for the recording oh and being wizards and being wizards that's also true arguably better than the actual show some would say i mean no one i've heard but i'm sure someone would say that and in the next episode keep an ear out for more news about the big macadamia nut and a bit more information about 007.

Thanks for listening. Thank you. Goodbye. See you next time.