A Problem Squared - 121 = Bi-annuals and Diagonals

Episode Date: November 10, 2025

🗓️ Does bi-weekly mean every two weeks or twice a week?🧊 What is the name of the line between two opposing corners of a cube?🕑 And daylight will be saved with some Any Other Brightness.For more on Rupert and Nopert Shapes:Euler Brick: https://mathworld.wolfram.com/EulerBrick.htmlTom7 - Rupert's Snub Cube and other Math Holes: https://www.youtube.com/watch?v=QH4MviUE0_sTom7’s Print files for Platonic, Archimedean and Catalan Solids: https://makerworld.com/en/models/1617011-platonic-archimedean-and-catalan-solids#profileId-1706419Follow Dr Ben Whittle, The Excellent Etymologist, on Instagram! @schnebwhittleJoey Parrish and his Sega Slides https://github.com/joeyparrish/sega-slidesSee Matt on tour! http://standupmaths.com/shows Specifically, see Matt in London on Monday 1st December! https://lwtheatres.co.uk/whats-on/matt-parker/ Or if you would like to see Bec in Brighton on Monday 1st December, tickets are here: https://www.komedia.co.uk/shows/john-luke-roberts-geoffrey-chaucers-mediaeval-christmas-festivitye/Here’s how to get involved with Matt’s Moon Pi Kickstarter: https://www.kickstarter.com/profile/standupmaths And here’s how to volunteer for Calculate Pi By Hand with Matt: https://forms.gle/w44THpNJ3jWUPqHy6Join us on Patreon for early releases and our monthly bonus podcast I’m A Wizard. If you’re already on Patreon and have a creative Wizard offer to give Bec and Matt, please comment on our pinned post! If you want to (we’re not forcing anyone) please do leave us a review, share the podcast with a friend, or give us a rating! Please do that. It really helps. Finally, if you want even more from A Problem Squared you can connect with us and other listeners on BlueSky, Twitter, Instagram, and on Discord.

Hello, Beck here, one half of a problem squared, just jumping in before we start to say that we will be sending out our Problem Squared Christmas cards, that's the digital or physical versions, to our Patreon supporters shortly. So you have until the end of November to sign up as a Patreon supporter if you would like our Christmas card either digitally or physically. Now, on with the show. Welcome to a problem squared, the podcast where I realized I've written the same introduction I've used before.

But I'm doing it anyway. Wait, how long before? Tell you what, I'm going to do the intro. And then we'll find out how long it's been. Okay. And if how much, because I've forgotten and how much. I overlap. Okay.

Welcome to Problem Squared, the podcast, which is a bit like daylight saving time. Oh. Yeah. Because we're pretty sure it solves some problems. I'm not sure which ones. Probably did a long time ago. And we keep doing it anyway in the hope it's helping someone somewhere. I'm Matt Parker, a lot like daylight saving time, in that I cause a lot of people to have

to do extra arithmetic every now and then. Nice. And I'm joined by Beck Hill, who is always... on time plus or minus one hour. Yep, that's me. There you go. I don't remember you doing this. No, I just had this feeling.

I'm like, wait a minute. Have I done this before? So I messaged producer Laura this morning. And I was like, have I done a daylight saving intro? She's like, yes, you have, you dingers. And do you know what's worse about that? Because Laura, I think, when did you start regularly producing for us? Beginning of the year.

Yeah. So you did a daylight saver's intro exactly six months ago. That's so good. at the last daylight savings. Brilliant. But because the clocks went the other way, it was slightly different. It was different.

It was different. The clocks were going to get the other way. I feel like it's topical and you haven't actually repeated yourself. So what did I say last time? We were recording remotely because one of you was in Australia and one of you was in London. I think it would have been Australia. Or it was just as you swapped over and we had real trouble organizing records around the time difference and arranging stuff.

So you said that daylight savings doesn't quite work timing-wise. across all the countries it covers. That's true. And also, when you introduce Beck, you said that she is like daylight savings because she brings a little bit of extra sunshine into everybody's life. And obviously, this time around, it's dark and cold and miserable. And you are right. I am usually off by an hour.

Usually in the one direction. Normally in the one direction. Yeah, yeah. And on this episode, I'm going to work out, which is correct, biweekly or biweekly. I'm going to go through some shapes. And we'll have any other, any other brightness. Yeah.

Any other business for any other new listeners. How are you doing? I'm good. I like daylight savings every six months. I co-host the main stage at Brussels Comic-Con. You do? Every six months? That's twice a year.

Yeah, yeah. Oh, my goodness. With the other mat. my life, Matt Highton. It was lovely. I do have to apologize. The lovely Denver, friend of the show, who the first time I met Denver at Brussels Comic-Con, he introduced himself by holding up a playing card and saying, is this your card? And I was like, we are going to be friends forever. Denver also came sixth, I believe it was, in the World Barista Championships. Oh, yes, to discuss Denver and their coffee making skills previously. Yeah, and he gave me some very nice coffee

beans from the cafe he works at to pastor you, which I have left at home. I about to say, I have not seen those beans back. No, no, I left them at home today. Because today I was, it's my birthday. That's my excuse. Oh, wow. I wasn't thinking about gifts format. I was wondering how long that it would take before we play that card. Near immediately. Well, I just figured it gives me an excuse. No one can get angry at me. Yep. Well, you know what my gift to you for your birthday is? Not getting angry at me. No, those beans. They're yours now. No, no, they're nice beans. And I plan on bringing them next time so that you can coffee with them.

So I can make them into coffee that you can drink. Okay, fine. They're your beans, but bring them and I'll turn them into coffee. But yeah, it was lovely. Got to meet some very cool. We had Christopher Lloyd again. Oh, I was going to ask you the big stars were. Yeah.

Christopher Lloyd. So that was nice. As lovely as before. Yes. We had Jamie Campbell Bauer who played Vecna in Stranger Things, the young, young Vecna. And he's in a bunch of other stuff. We've had him as a guest before, and he's so, so easy to get along with, so easy to shout to.

And so it was really nice because it just feels like you're catching up with a mate. To the point that Matt and I always forget how popular he actually is, and there was already some fan accounts that had put up some footage of the interview and stuff, and we're like, oh, yeah, that's rude. He's got like 3 million followers, okay. Just nice time, nice time all around. Oh, lovely. Also, got to catch up with Boudi, who had come along to see my.

show in Edinburgh Fringe and had come with his friend who had heard of you. Yes. And I was like, yes, definitely. Saw me after my show. They went and saw you. But he came along to the Comic Con and I was able to ask him what he's been up to. He's done a falconry course because he's scared of birds and wanted to overcome that. I just love it.

I love when people come up and they're like, hey, I've been listening and keeping up with what you're up to. It's nice. It's really nice. Good friendly folks. Good to hear. How about you? Good. A small break in the tour.

Mm-hmm. Well, we've got one more on the 1st of December, the big London one, very excited about. Yes. Everyone please come along. Yes. Because the venue's 1,200 tickets. If it's sold out by the time you listen to this. Oh, there's no way.

There is no way. There's a zero percent. Maybe like on the day. Oh, and the tree's working. There's an update. Oh, just in time for Christmas. Tree is online for Christmas. Yep.

We had a big work hang. a maker hang I had Seb and Abby came around to the new studio Oh yes The Nudio

where we had space in the Nudio to spread out all 500 LEDs and we totally rewired the power supply for the LED so we were here

soldering and gluing and assembling and doing all sorts of fun stuff because if anyone saw my previous show Humble Pie

Seb and Abby did the lasers in Humble Pie and Abby is on tour taking care of the tree and we had a wonderful day. We had a full day just making electronics and testing LEDs and software. Then we've got the hardware is all now.

So lovely. Oh, that would be nice. Oh, it's so good. I hacksawed down the base of the tree and I permanently attached it to a lazy Susan to the whole tree rotates on the spot. It's so, it was a great day, great day. And it was wonderful use of having a bit of extra space in the new year. And then we've got the software, I've updated my old software.

where we've got plans for better, but it's now it's on its feet. It's just, it's taken along. I've kind of forgotten how much fun it is to hang out with friends and build physical things. I mean, the issue I have is now already we're thinking, I was like, oh, we could do bigger. Like, we could get more lights on a bigger tree. That's generally how it works. Yeah, yeah. Yeah, you've got to get to a point where people want you to do the Christmas tree lighting in a town,

but you're running, like, it's a whole big, mass thing. Yeah, yeah, yeah, where everyone in the town gets together. You know, like your pie stuff. Yeah, and I got some free time in about 2029. Yeah. So we'll get right on to that. Hey, don't say 2029, because you know for a fact you're going to get asked again. Oh, someone will write that down.

Don't write that down. But anyway, building physical things, the other thing I came across that reminded me how wonderful that was. I went and spoke at a conference last week. Time has no meaning anymore. I think the one thing we've learned from this is your memory is. Good shot. Yeah. I think I do more things than I can move into permanent memory.

That's the problem. It's a bottleneck. I was at a conference called Demuxed, which is for video devs. People who, software developers who work on video streaming services. And I was the last talk of the conference. And I was chatting about my adventures in coding and the like. And you know what it's like when you go on to do your spot and then before you, which in this case is just a speech.

at a tech conference. Yeah. Just like blows the gig out of the water. Yeah. And then you're like, why are they on right before me? I was on after someone who presented all of their slides off cartridges in a Sega Mega Drive.

A Genesis, Sega Genesis for our North American friends. So, yeah, he had a converter. So he plugged in a Mega Drive on stage. Yeah. Had a converter because the old video out had to be converted to HD. MI to go into the system. Yeah. And then he had a series of numbered cartridges because you can't fit that much on a cartridge.

Right. And he would put a cartridge in and turn it on and then a slide would come up and then he'd used the Mega Drive controller to advance through the slides on the cartridge. That's impressive. And I was like, I've got to up my hardware game. That's incredible. Engineer called Joey Parrish. And Joey also had a heavily modified cartridge which he'd added some extra chips and Wi-Fi.

that could stream video to the megadrive. Oh. So he could play. You have to run it through an encoder first to encode it into a format the megadrive can understand. So is it like pixelated? Oh, you're so pixelated. There's a lot of interesting constrictions on color palettes.

Yeah. On old systems. Because technically there's 256 colors, but you can only load so many in a palette per. Right. It's not even per frame, per whatever. But he'd written an encoder that would pick a different color palette per scene. So the encoder has scene detection. And when a scene changes, that's when it would reload a new color palette, which visually looks a lot better.

And obviously, the sound is super compressed. Wow. Phenomenal. This reminds me of when, didn't Michelle Gondry, the director, helped build the software that turned footage into Lego? Fell in love with a girl white stripes song. The video for that, they used a mix of genuine stop motion. and stuff with Lego. They had to like build it, like physically build it based off the frames and the video and then teach the computer to understand what it had done. Right. So it could then

Plastic machine learning to then do the rest. Yeah. Yeah. Similar thing. Running it through a pointless bottleneck for the sake of it. Because the cartridges by default fit like 13 seconds of video on them. Wow. So we had to have an extra thing that's, what it's doing is it's constantly, there are two kind of memory chips on the cartridge that the console can be looking at. And whenever it's looking at one of them, this extra processor he's got like sold it in swaps the contents of the other one. And then by the time it looks at that one, it's swapping the first one. So as the chips looking, the mega drives looking at this one and that one, he's like, oh, this is all new.

Oh, this is all new. And that's how it's constantly feeding in more of the video. It's very, very clever. I love that. It's like how you would distract a baby. Yeah. Yeah. Yeah. It's a bit like how the angels would attack in Doctor Who. Exactly like that. Whenever you look away, the memory content swaps. Oh, well, that's fantastic.

Yeah. So that was my highlight recently. Was watching someone give a presentation entirely off Mega Drive Cartages. That's a good highlight. All right. Well, should we start doing our own highlights. Yeah. First problem was sent in by Ahmed, who went to the problem. and posing page at a problem squared.com selected problem from the drop down menu and typed hi beck and matt i like to consider myself fluent in english well so far so good i agree oh even though it's not their first language yep however there's one word which has been really annoying me recently

which no one seems to agree on what it means i mean that's not narrowing it down armad there's so many words in the english language you could be talking about but it turns out they're talking about bi-weekly. Bi-weekly. And Ahmed complains that some people define it as twice a week, while others define it as once every two weeks. Armad then decided to check bimonthly. Oh, I'm so sorry. Do they check, like, biannial?

Ah, they did. They say here, out of frustration, they check the yearly version of it. And this is where things got a bit more interesting. At first, they found out there's biannial and bi-yearly. which seem to be used interchangeably. And they've also got biennial, which specifically means once every two years. So seems to mean there's hope.

With this bit of knowledge, Ahmed then tried to go back to monthly and weekly to see if those variants made any more sense, but they had no luck. And so, their problem for you, Beck, is they wonder, what was the first intended meaning of these words on record? And if we know this,

can we definitively and conclusively say, what's the correct use? I think specifically they're talking about bi-weekly here. And Armid said as an added bonus, could we come up with new words for the second meaning? Interesting. Beck, what have you got? Well, I did some research because this also bothers me, especially as this podcast is either bi-weekly or not bi-weekly, depending on your meaning of bi-weekly. Yeah.

So this has bothered me as well. I'm sure it bothers many. about other listeners. So I did some of my own research and couldn't really find anything definitive. Can we just quickly clarify some words here? Yes. Biannial. Yeah. And biannial have different meanings. Biannual can mean the same as biannual. But biannual does not mean the same as biannual. Okay. So what does, so biannial has one meaning. Biannial means specifically once every two years. Got it. And that's like an e-enial. Got it. Okay. By annual, should just mean the other one.

Yeah. Twice a year. Yeah. But can sometimes be used to mean every two years. Yeah. And by yearly, it can go either way. Even though we got perfectly good other words, that should make this unambiguous. Mm-hmm. Okay. But then there's just biweekly and bi-monthly are just doing their own thing.

Yeah. Okay. So, after doing some research, not being entirely sure. I thought, hang on a second, I know an etymologist. He's helped us on previous episodes. Bring him up. So I reached out to Dr. Ben Whittle, who is Schneb Whittle on Instagram. We'll link to his Instagram in the show notes.

And he said that it seems, according to his research, that twice a week was the original meaning of biweekly. Right. He says even the Oxford English Dictionary and Miriam Webster Dictionary both agree it is ambiguous and confusing. Correct. No one's confused about whether or not it's confusing. Yeah. Miriam Webster says to quote, The chief difficulty is that many users of biweekly assume that others know exactly what they mean and they do not bother to clarify.

Yep. Yep. Now, I thought this was fun little bonus fact. Dr. Ben Whittle also added that random etymology that I didn't ask for. The buy bit is related to Biss in Biscuit, which means twice cooked. How great is that? That's great. I had no idea.

That's where the term biscuit comes from. I want to give Dr. Ben a shout out as well. He's very funny on social media as I was going through my flat and reorganizing it. I found in my costumes box, as we all have, a captain's hat, you know, like a ship. Well, like a sea captain's hat. Yeah. A captain's hat and it's got an anchor on the front. Classic. But it says Scientologist. Oh. And I don't know where I got it from. I don't know where it comes from. Yeah, I believe you own that. It's one of those things where you go, okay, I have no memory of where this came from. and I posted about that on my stories

and Dr. Ben replied to me and said you sure you didn't get it on a Tom Cruise and it was the of all of the Oh you word nerds I had so many comedians respond and none of them was funny

Tom Cruise Yeah an etymologist That's where the Yeah Yeah so give them a follow So that's that's the official answer is that apparently

biweekly did a in the very first record of it, meant twice a week. Now, I think that makes sense because I would use, if I meant every two weeks, I would say fortnightly. We have a perfectly good word for that. Yeah. Before a video game took it over.

Yes. Do they say fortnightly? Well, Fortnite is not really used in North America. But it should, but I'm saying we introduce. It should be. And Fortnite used to confuse Americans. But now it's, please do. correct me if you're a North American type of person. Now it's more closely associated with

the game. Fork knife. Yeah. So I say American listeners, Northern American listeners, basically anyone in a country that doesn't currently use fortnightly. If you're speaking English, please use fortnightly. Get that spread. Yes. Portnightly, I say we call it. Fortnightly is every two weeks, bi-weekly is twice a week. We just all agree that that's the case. If you say bi-weekly meaning fortnightly, that's on you. I mean, if biennial and biennual have taught us anything, having another option does not stamp out all the ambiguity.

So you're thinking maybe we just phase out biweekly altogether. It's too confusing. We've got fortnightly. So what should the twice a week? Tweakly. Twinkly. Twice weekly. Yeah.

Tweakly. Because you wouldn't say twice weekly to mean... Every two weeks. Every two weeks. No, that'd be twockly. Yeah, exactly. Tweakly and Twikly and Twokly. Now did it.

Okay. I'm now getting rid of Fortnightly. Twinkly, twice a week. This podcast comes out Twockly. Yeah. Tworckley, it's done. I'm on, I'm sold. I'm sold. I don't think we're going to be twockly. Like, the amount of fun it is to say, everyone, wherever you are right now, say Twockley, out loud. It's really fun. Twockly. All right, Twinkly and Twakley, or two clee if you want to,

but you can't, we'll accept all pronunciation. How can we be arguing about the pronunciation of a word that was invented about 60 seconds ago? Producer Laura, can we change the description of our podcast that it's released Twockley yes we can great now

now but that means the description of our podcast will be forever like let's say Twockley catches on yeah that would be the original citation of first use

that's the one that would get notated in all of the the wiki articles first used 2025 description of a problem squared yeah so So if we could get just some more people using it in an official setting.

Yes. So that there are more instances. If it's just us, I'll go back to Dr. Ben and see if he can. We'll see what Dr. Ben says about our invention. So we've got, well, firstly, we need Ahmed to say whether he appreciates. Twinkly and Twockley. Now, obviously, we've got the monthly versions as well. Now, interestingly, most months are roughly.

four weeks long oh so if you were to do something fortnightly you're already doing it twice a month twomply i say that there are sometimes moments where we have three episodes come out yeah because they're four point four and a quarter weeks long yeah yeah so that so so twice a month is subtly different to Twinkly. Yeah. So if you do have something that specifically comes out twice a month, not every two weeks, but twice a month. Yes.

Because we're not twice a month. Yeah. We're Twockly. That's right. And twice a month would be twynthly. Even you weren't confident. Tweakly and Twinkly. So then we need twinthly and twonthly.

No, I don't know. Like, officially, we should say, yeah. Byweekly means twice a week and fortnightly means every two weeks. Yeah. In the same way that biannually would mean twice a year. Biannually would mean every two years. However.

However. People will still get confused. They get confused. Hence, tweakly and twigley. Twigley, twigley, twilly, so it would obviously be tweely and twiolly. Now, are there, are there? Because we've got the word two. Tworly. We're using two for Twinkly and Twokly.

Yeah. Buy, meaning two, is around. Is there anything else that means two? Duo? Jewel. So maybe we could use Duo, so we could use that for monthly, just to keep everything crisp. So you've got Dumfrey? D.

Which one is Dumfley? The one it sounds like. Obviously And jollfully They're very different word Okay, maybe that's not going to work What we could do

Why we're making sweeping reforms Is Make Months four weeks long Do that Your There's a little bit of scope creep happening here. Your answer is to completely

reinvent the calendar. Yeah, retool the calendar. It's about time. Yeah. Sure. Why not? Thank you. Thirteen, four week months. It's all I'm asking. I like Twinkly and Twakley. Yep. So Twockly and Twonthly. Twotly and Twoncly. A very similar periods of time. And then twirly and twirley and tworley how we made it worse it's worse now look that's my answer and as far as I'm concerned

Ahmed is the person who I am trying to appease here now if Amid turns around and says as someone who speaks English as a second language that is too similar that is too confusing but I would say it's still better than having one word that means both Agreed, agrees. Agreed.

Fine. I'm happy for Ahmed to be the adjudicator of this. What are your... I'm on board with Tweakley and Twakley. I feel like we've nailed that. Yeah. I don't think anyone's going to have any notes. Uh-huh.

I just think biennial and biennial already exist. And people get it wrong. There's how much we can do about that? We've got two perfectly good words. I don't know. The monthly, I think we just change the length of the month. I think that's the, that's the easiest solution here. Does that change the length of the year?

No. It'll be, what you would need to do is have 13 months each with four weeks. And that's your 52 weeks. Which means that we need a word for 26. weeks, which would mean twice a year. Yeah, yeah, yeah, exactly, yeah, yeah, which would be halfway through a month. If you were releasing, let's say this show, let's say we put out... Oh, yeah, yeah.

And a problem squared every 26 weeks. Is there ever a chance that that means that it would be more than twice a year or less than twice a year? Oh, got it. Yes, eventually we would put out three in the same calendar year. Right. So that is an issue. It's the same thing. So we have to change the length of a year. We have to have a bonus day. You have another made-up day. Or do we just say years and now 52 weeks, exactly. No, we can't do that because we're tethered to the orbit. Oh, why do we have to do that? I know. It's a bit like daylight saving in that regard. Oh, God. The Western understanding of time.

It's the worst. It's too, too consumerist. Yeah. At the end of the day, everything is just going to going to deal with the orbit at some point. Okay. Yeah. It's where you put the fudge factor. I love that show. You know, fudge factor. That would be a really great, like, master chef meats, like eggs, like, you've got to make

really good fudge. Yeah. That's all it is. Yeah. Not being judged. Yeah. I'm on board. I would judge that.

It would come out twuntly. Stop trying to make Twantley a thing. I'm looking forward to all the mean girls memes now. So, I'm at all of that, let us know. Yeah. Now, look, there's going to be a lot of people writing in, suggesting better suggestions. I say better using verbal quotation marks because there's no way you're going to be tweakly-tweckly. Twently, Twonthly or Twirley and Tworley.

We twirley can do better than that. So don't bother sending your better. Don't. You're not going to win. I mean you should. But, oh, you'd have to be so sure it's better than that. But if you do agree with me, just start putting it out there. Go to the problem posing page, select solution, and just tell us about the different ways in which you've used it.

put it in the problem squared discord put it in the problem squared reddit great amette get back to us let us know if it's a towing is that dinged twice a problem yes or a ding every two problems no that's a twong oh sorry this next problem is this next problem is is from Y-O-U-P, Y-O-U-P, I hope I'm pronouncing that correctly. They say, my son asked me the other day what the line was called between two opposing corners of a cube. All I could come up with was that in a circle, you would call it the diameter. Yes, in Dutch it's the same name. Ah, it's a Dutch name.

Google didn't help me out, but I'm pretty sure between the two of you, you know, a lot of measures other than Bex. Yes, also Dutch. Yeah. Thanks for all the joyful hours of ear noise. Oh, what a wonderful. That's why our description says, releasing ear noise. Twockly. Tworckley.

I like this question because this is the exact sort of thing I would think, hang on, what is that called? Yeah. Yeah. It's a real, what's the name of that thing episode? Yeah, because what would you say? Because obviously in a circle, it's the diameter. Yep. Would you say diameter in a sphere?

In a sphere, yes. Okay. Anything circle, sphere, etc., which are all part of the one big family, you'll say diameter piececake. People will sometimes contrive diameter to mean things for other shapes. Right. And so it's not meaningless with other shapes, but there's less of an agreed upon. That's the name. Like biweekly.

Like biweekly. Yeah. Oh, actually, I'm going to grab a cube. It's right behind you. I'm just going to grab it now. I 3D printed a cube, which is like the biggest misuse of the abilities of a 3D printer. But hold it. It's a really satisfying cube.

Like, if you ever want a really nice cube of a very specific size, look at that. Yeah, that is. It's quite sharp on the corners. Real pointy corners. It's a good cube. Yeah, it's a good cube. But the reason I printed that cube was a tesseract. A tesseract?

Oh, not quite. What is a tetheract? A 4D cube. So if you went up a dimension, that would be even more cube. Whoa. Yeah. Well, you know you're looking at that cube, and you could think about it, you're looking at six squares carefully arranged. Yes.

A tesseract is a 4D cube, which is eight 3D cubes carefully arranged. So it's a very similar thing, one dimension up. Sure. There you are. Every time you go into four-dimension chat, my brain's like, that's why I gave you a thing to hold. Thank you. I see what you're doing.

You're distracting me on one side while you move on the other. But the reason I 3D printed that cube was people recently found a shape that can't go through itself called the No-Pit. And so I also 3D printed this cube, which if I reassemble it, here we go. This is a cube in two pieces. So that, actually I had this over to you as well, if you want to have to play with this one. So that's a cube that's exactly the same size as the white cube. So I wanted to have two identical cubes, but one comes apart and one doesn't. So you should be able to remove the inner section of the green cube.

Yep. And the identical sized white cube will fit through that ring section. Ah. So what we're demonstrating is a cube is able to pass through another cube. There you are, look at that. Mm, that's very pleasing. Of exactly the same size. Because a long time ago in a very old episode, near when we're first starting out,

was a Halloween episode where you carved a pumpkin. Exactly this. Yep. Pumpkin of the same size could go through it, I believe. That's the one. I bought two as identical as I could find pumpkins to make, this is called Prince Rupert's cube, and the property of going through itself is called being Rupert.

That's the property of this. What? Why? Because a guy could Prince Rupert came up with a question. Okay. And like, I think the 16, 1700s ages ago, Rupert was just like, hey, I wonder if a cube can go through itself. Sure.

And the answer was yes. Prince Rupert's like, I'm just going to think about ridiculous maths and science things. So that's pretty good going. Yeah, if you're going to use your privilege. Bingo. So we call it the Prince Rupert cube. The property are going through itself is called Bing Rupert. And so I made a Rupert pumpkin for Halloween 2021.

He's going Rupert! And so I made a video about a big Rupert. So a friend of mine, guy called Tom Seven, was working on proving shapes exist that aren't Rupert. He called them the property being Nopet. Excellent name, Tom. And he's been working on it for ages. I saw, I was in, he's, I'm in the US. I saw him when I was in New York a little while ago.

And so, back then he was working on it. And since then, someone else beat him to it. No. Unbelievably, a different team of mathematicians were working on the same problem he was working on with his mates. And so out of nowhere. And they had, they converged on almost identical methods. But he was trying to prove that a snub cube is noop. Sorry, a snub?

No, I thought you might say that. So guess what I've got for you, fresh off the 3D printer plate. Oh, you're going to snub me? Okay, so I'm currently holding. Oh. So the best I can describe is if you could turn a cube into a constantina where you pull it out by twisting it. And it creates a bunch of triangles in between. And then, so is there a way that you can twist it and the triangles would fold into each other and go back into a cube?

Yeah, pretty much. Could you make that with paint? paper. Oh, you would need to have some edges not joined and I don't. My instinct is there would be space for them all to fold up out of the way, but I couldn't go and do that. Well, we can look into it. Someone's got a project. Yep. So that's a famous shape called a snub cube. I'm a big fan of it. And what Tom 7 was trying to do is prove that the snub cube is no-pit. We will put pictures of all of these on Instagram, Twitter and Blue Sky. Actually, on the shelf over there

behind you is Tom Seven's NoPitt. If you want to grab that ridiculous looking shape. I wasn't expecting this to be a whole segment about NoPets. But given we did cover this topic, 2021, this is like within the Apollum Square universe. Noopit is, you know, an active

thing we talk about. Oh yeah. I also I like that sometimes, because I imagine you're doing a video about this, which is why you have 3D printing. That's why I printed them all. I like that sometimes this podcast serves as a sort of director's commentary. It is a directs behind the scenes. I think they support. They support each other quite well. So this is what I'm holding feels like it's almost got the vibe of like a cartoon diamond without a pointed bottom. But the triangular shapes that would join. up are not equilateral isosceles even they're sort of a bit odd and then one of them isn't even a triangle and then you've got a pentagon at the top and the bottom yeah what a strange shape yeah

so that's no put candidate number 214 so this can't pass through itself we believe well no one's found a way for it to pass through itself so i forget exactly how many on the order of six trillion attempts using Tom Seven's code, there's no way to find how that will go through itself. And when he applies the same code to shapes that can go to themselves, that finds the solutions in fractions of a second. So the fact that it cannot solve this one, we're almost certain that it's no-pit, but it's not been proven. Yeah. And the snub cube, we're almost, it cannot find a solution for that. So we're pretty sure that's no-put. And Tom 7 was working on proving, because you can't just check loads of times, you've got to prove you haven't

like, you've not missed the one solution. Now, most, I would argue that most things are no-put. That's very true. We're talking specifically convex polyhedrons. So, shapes with flat faces and they don't have any dense in them. So classic polyhedra. Is this one of those examples where. it's not necessarily obvious as to how this is useful.

Oh, it's very obvious that it's not useful, but carry on. But the processing power, I mean, not just like computational, but also just human processing. The way you have to think about this problem does then mean it tends to play off into other ways in life. We tend to find uses for things or whatever. that we're like, oh, turns out that's really useful to have worked out. Agreed. It feels very unlikely this specific knowledge about no-pateness will have practical applications, but it cannot hurt for humans to have a better general understanding of 3D shapes. And potentially, people working on the problem could come up with new, you know, computer

numerical method techniques, or then take what they learned from this and apply it to a different problem that's useful in terms of their, you know, solving problem skills, etc. In general, it's not like this was a problem we desperately needed the answer to. No, but in the future, when we are under threat because AI wants to put us through ourselves. Something like that. Yeah. Yeah. And I mean, the point that Tom 7 makes is the notion of a polyhedron is pretty standard. So, Were there aliens who have also evolved to the point of doing mathematics, they would definitely would have discovered the snub cube because these sorts of shapes just kind of drop out of maths. And the idea of can something go through itself is also an interesting question that humans have

been wondering for centuries. This feels like a Netflix show in the like, is it cake or like that YouTube series? Will it blend? Yeah. Will it nope? Will it no. Will it rupert? Will it rupe it? But I imagine aliens have asked the same question about is something.

They'll have a different name for it, of course, but this concept of will a polyhedron go through itself is a sufficiently obvious question that other intelligent species probably ask the same thing, which I think is an interesting thought experiment. Anyway, which is a very long way to say, the people who beat Tom 7 to the punch, instead of... Tom 6, wasn't it? I knew it.

The higher rank. tanked Tom. Instead of using a pre-existing shape. So the one you're holding, Tom Ranley's code, and then also generated random shapes to find ones that couldn't be solved, and that's where that came from. But then he used a pre-existing shape, the snub cube, to try and prove something is definitely no-put. The other people who beat him, they manufactured their own no-put candidate in such a way that it would make the proof easier, which is a very clever way to go about it. And they were then able to prove the shape they generated is no-put. So very interesting maths. So I'm making a video on that with wide 3D printed a cube.

And there you are. So that's the Rupert update four years later, which is a long way to talk about the actual question. Oh yeah. The problem sent in. I forgot about the question. But speaking of things we don't know the answer to, the problem sent in by Yup does actually also. relate to an unsolved problem in mathematics. Now, it's not the name. We have a name.

Okay. So when you look at a cube, there's a couple of different diagonals you can talk about because you could have the diagonal that's just on a face that goes from like a corner to another corner on the same face. Yep. And we just call that a diagonal or maybe a face diagonal if you want to get specific. The diagonal that goes from one corner to the opposite corner is called the space diagonal.

Which is a great name. Or spiagonal. Or spiagonal. It's not called that. So the space... No, it is. We can't just keep cracking out new words any time we want. Well, that's how everyone else does it.

It's so true. Can we get some reverb on this as we go... Space diagonal. Yes, we can. Diagonals in space. Yes. So, oh, the Rupert cube... follows pretty much the space diagonal when it goes through the other one.

Yes. And that's why there's enough room. Because if you look down the space diagonal, a cube looks like a hexagon. Yeah. And then you put the square face. The square face of a cube is smaller than the hexagonal view down the diagonal. And so the open problem about the space diagonal is people have found. Now, we're going to relax the definition of cube.

So we're just going to talk boxes in general, cuboids. So it doesn't have to be the same. same length in every direction. You have three different lengths for different directions. People have found cuboids that have integer length edges, the three different edges, so they're all whole numbers. And all the diagonals, all the face diagonals, are whole numbers as well. It's like the 3D version of a Pythagorean triplet. Okay. They're called oiler bricks. Right. So an oil of brick has whole number lengths and face diagonals. No one has ever found a perfect cuboid where the space diagonal is also a whole number length.

And just to double check that I'm understanding this correctly, by whole numbers you mean like if I was to do a cuboid where it was like three by seven, the diagonal might be then like four. 0.6 and it's the decimal that makes it non-integer makes it right. Yep. So if your cube is like one by one the diagonal is 1.4. Got it. But if instead your cube was like 3 by 4

the diagonal would be exactly 5 nice. Oh, that's lovely. No one's ever found a perfect cuboid where the space diagonal is also a whole number. But no one's ever managed to prove it's impossible. So we don't know. It might exist, it might not. That's the mystery.

of the space diagonal and then you put reverb on that I loved all of that there you are I mean I could have answered it in literally two words I could have just said

space diagonal oh the less fun but I feel like you know what not enough ear noise not enough ear noise and youpe specifically praised the ear noise

yeah there you are so youep let us know I mean I think it's pretty pretty I mean that is the name that's the name I've given you the name

I do you know what, on behalf of you, but I'm going to give that a space ding. Hang on. Sorry, I'm going to give it a space ding. And now it's time for any other biannialness. Albert wrote in when we were tackling the problem about the snake and the probability of rolling snake eyes. We referenced the snake draw, but we didn't know what it meant. Albert knows what it means, which is why Albert went to ProblemSqured.com and picked solution and told us a snake draw is when two captains take turns to pick teams.

But to negate the advantage of picking first, instead of alternating Captain A, then B, then A, then B, then A then B, you do Captain A picks first and then B picks twice, and then B picks twice, and then B twice. Oh, interesting. So it goes A, B, B, A, A, B, A, B, A, A, B, A, A, now. First of all, Albert, thanks. That's what a snake drum means. There's a sequence in maths called the 2A Morse sequence. Ah. And 2A mors is to solve the same problem, but it goes A, B, B, A, but then if you just keep doing that,

it's still not exactly fair. So what you do is you then flip it. So you do A, B, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, B A, B A, B A, B A B, B. Really? So if I said right, left, you know, meaning I'm holding the sticks. Okay, yep. But I'm going to change it for A-B, so to go A-B-A-B-A-B-A-B-B. I believe you.

I A-leave you. But then you take the whole sequence again and flip it another time. Oh. So then, so it goes A, B, B, A, A, A, A, A, A, B. And then it goes B, A, A, B, B, B, B, B, B, A, B, and then you take that whole sequence and flip it. And as long as you need a sequence, you just take whatever you're, the first one. And if you scale it right back, it works from the beginning, because you do A, and you flip that and add it on the end, you get A, B. And you flip that and add it on the end, you get A, B. And you flip that and add it on the end, you get it. a BBA and then it just builds up recursively the whole way through. So, there you go.

You also heard from Rob, who says, I was listening to your episode 118 about kids' names that can be grouped together, and it made me realize that my wife's and kids' names all overlap and come together into a Megasaur name. I love the use of me. I'm here for it. I love it. So Rob says their wife is Lisa, the kids are Sam and Eli.

Oh yeah, so the L.I overlaps with Lisa nicely. Yeah, so we've got, or Eli, Sam. That's very cool. Yeah. It's just the two kids' names in a row has the mum's name in the middle. Yeah, that's really nice. And I love that you realize that. Rob, you're letting down the team.

May I suggest changing your name to Amy, which would fit on the or at the beginning, Mel. Oh, Mel would, yes, producer Laura just mentioned Mel. And then it would be Melisam. Come on, Rob. Melisam does sound like something you would take to like up your cortisol levels or something. Take Twockly to improve. But not tweakly.

Take. Do not take, Melisam. We cannot be held responsible for the results. Just someone running out of a bathroom covered in hair. Rob or Mel slash Amy also said that they loved your show in Edinburgh, Matt. Ah, that's very kind of them. Yeah. With you're still touring?

Still touring. Come and see me. Link in the show notes. Please come and see the London gig. Well, we've reached the end of the second ever daylight saving special edition of a Problem Squared. All that's left is to thank a few people. Thanks to you, the listeners, for listening, which by definition you are right now. We really appreciate that.

And thank you for all the five-star reviews. You give us on multiple platforms, tell your friends. And huge thanks to our Patreon supporters who not only listen, but hand over their hard-earned money. They put their money where their ears are, and they keep the whole thing ticking along. and to thank them. Among other things, they do get an exclusive monthly podcast, which is not as good as this one.

I would argue it's better. Would you? I'm a wizard, I think, is... It's something. It's definitely more something than this one. I think it's raw and unadulterated. We agree with that, and we draw different conclusions from it.

So, in addition to all of that, we pick three names of our Patreon and supporters completely at random. There's no memory, by the way, and people say the name hasn't come up yet is totally random. And people have come up multiple times. That's randomness. Yeah. Them's the brakes.

The only way to get involved is to get involved. You create multiple backgrounds. Multiple times, yes. If you signed up several times. Yes. And then you increase your chances of having your name read. Buy more tickets in the lottery. The winners of which this time include...

Jay Honad Am's. Yeah Need dem an Shah Shah Lai Goodly So that's it for the episode Thanks for listening

I've been joined by Beckhill I'm Matt Parker And producer Laura Grimshaw is a bit like Daylight Saving in that she keeps us on time thanks for listening bye

F2 F2 miss and you may luck and you may luck would run out eventually And I'm going to... Ooh, I finally completed my diagonal pass. I guess A-10.

Hit. Oh my goodness. Oh, that's interesting. I don't think there is any way I can win this unless something goes horrifically wrong. What's about to happen, yeah. This is where you find out that I've illegally placed one diagonally. of them sticking out of the side of it.

Oh, no lucky, got real lucky. You have no idea how much I was hoping you would go for J-1. Yeah, I know. Well, happy birthday to me.