Can you make a hole in a thing bigger than the thing? 

A Problem Squared is a great podcast, I’m glad it’s been giving you so many ideas! PS. if anyone hasn’t listened to it yet, I’d highly recommend it!

Like cutting a sideways 2x4 slot out of a 2x4 plank then shoving it through. Or taking a door off it’s hinges and bringing it through a doorway

Do that with a sphere and I'll really be impressed.

And there I was thinking this would involve some topological trick and cutting out a funky spiral that unfolds (without stretching) to be much larger than itself.

Depends on how you define "the thing", "hole", and "size".

Rather than 3d printing one solid cube and one cut-out cube, you should print two cut out cubes and show that either fits through the other. That would be a cool party trick!

2021: Discovery of the Parker Pumpkin - A pumpkin that can be proven to be able to have a hole cut in it larger than itself, but not really because it can only be proven by putting another completely different pumpkin through it.

That settles it, I'm putting pumpkin scraps on my front porch and calling it the 'Parker Pumpkin' AKA Matt-O-Lantern.

4:18 you missed an opportunity to say "with the power of buying two" and connect with Technology Connection channel

I object to this use of the word "bigger". Surely a hole in a 3D object is also a 3D space, bigness of which should be characterized by it's volume, not by an area of any of it's projections. By the same definition you could take a piece of paper and argue that it's "bigger" than some lamppost, because you found a projection with a smaller area. This stunt with a pumpkin only seems interesting because pumpkin is a pretty close to a spheroid, if you did this with something more irregular, like a book for example, there would be nothing impressive about it, and you would hardly convince somebody that the hole is bigger than the book because you can fit another book of the same size through it.

I’ve always heard this is why man-hole covers are circles instead of squares. Otherwise, the cover could fall into the hole.

cutting a hole in a sphere wouldn't work , correct? because it's projection is the same no matter the angle.

This is like the adult version of those kid "puzzle" toys where you have to fit the shape through the right hole.

Matt proves in math, that a couch, can fit through a door way. Essentially

if you define a hole as the absence of something, then you can't have a thing be more absent than completely absent, away with your math sorcery.

This reminds me of the manhole problem, "why is a manhole cover a circle?" it's because that's the only flat shape you wouldn't be able to drop through it's cross-scetional hole.

ahh.. the ever popular.. visual demonstration on a podcast.. brilliantly done Mr Maths. Or can I call you Stand-up?

This reminds me of a story my granddad told: As the machinist at Rice U in the '50s he would machine parts according to blueprints given to him by students. One time he handed the student a pile of metal shavings noting that the Outer diameter and Inner diameter measurements on the drawing for a metal ring were reversed. He started with a metal disk with a hole in it and increased the inner diameter until the whole disk was gone.

That ended up being a little more interesting that I thought it would be. "Bigger" is a bit vague of a term, and I was thinking of the pumpkin as the surface (rather than the volume) because that's how you normally think about carving pumpkins, with the "size" of the hole then being the surface area of the hole. And of course you can't cut out more surface area than there is surface area - right? I thought you were going to somehow do (or redefine) the impossible. So when you started talking about cross-sections and what you actually meant by "bigger" I was kind of going "well, duh," at least for a spheroid-like object like a pumpkin. But those 3D printed platonic solids actually end up looking really cool and a little less intuitive than a spheroid.

Me: damn how's he gonna prove this? The pumpkin's gone. Matt: second pumpkin Me, terrified: How could you do this, we trusted you. The real demon was the parker pumpkin we found along the way.

Whoa. I came here from A Problem Squared to see if there's a link to the photos here somewhere, and I come to this!

Kinda neat. I thought this was going to be something like the question "Can you cut a hole in a 3x5 notecard big enough for a person to walk through?" I love showing the kids I teach how to work that one out.

Well, the first five minutes were definitely a parker square of an answer.

I thought this was gonna be the trick where you cut a hole in a postcard that can fit a person through. Though that one does involve folding the paper.

I'm loving all the remixes of the theme song recently.

This is essentially the inverse of the manhole cover problem. What shape can you use to never drop the lid down the hole?

This reminds me of the thought experiment "Can you crawl through a sheet of paper?" Wherein one is challenged to cut, without separating, a sheet of A4 paper. The key is to fold the paper down the middle, then cut on alternating sides in a comb pattern. Then open the paper and cut down the center. You end up with a hole in the center of the paper that can be expanded to easily fit a person. Boom.

"This is what the sun looks like in England in October" imagine being in October for ever

So a sphere I guess is the worst-case scenario with zero clearance?

I used to think about this puzzle a lot. In the game Portal, the portals are vaguely elliptical and about a 2:1 ratio. This got me wondering, if you took a board with a portal on it, you can orient it to fit through a second portal. I can't quite wrap my head around what would happen if you actually did this, though

I thought you might try to cut a spiral all the way down a pumpkin then use it to stretch it upward until the stretched spiral hole is big enough to fit the original

I think this was a silly interpretation of the question and I disliked the video, but I would never give a Stand-up Maths video a dislike because I respect the channel too much. Instead this negative comment exists to support you in gaining the algorithm's favor. Bless the maker and his pumpkin.

They do this all the time with those pressure cookers that make me cry because I can never get the lid in or out

This kinda touches on the reason that manhole covers are circular: it's the only shape that you can't fit through itself no matter what way you orient it. Non circular manhole covers would be able to fall into the hole, which would obviously be a problem. (To be real, they're probably circular because you don't have to rotate it to put it back in place. But the fact that it can't fall in is a nice bonus!)

"Same size cube, that's actually a bit smaller, fits right through itself." Who would have thought. ;)

I once climbed right through a hole in a playing card : ) It's pretty cool... you fold it in half, then make cuts from alternating sides as close together as you can. Finally, snipping up the centre of the fold (but leaving the very end pieces intact) it can be opened up into a large circle. I won a few bets as a kid with that one. On holiday I once tried to see how large I could make a hole in an A4 sheet of paper - using a craft knife and a steel ruler to get the cuts very close together. It was big enough to go right around the outside of a luxury (family size) static caravan that we were staying in at the campsite.. I might do one later... even at 50 I'm still just a big kid : )

Next obvious question, does this work in higher dimensions, and does the amount you need to cut out go up or down relative to the size of the object I'll see what investigating I can do, and edit this comment if I find anything interesting

"What happened to Matt's pumpkin?" "He did maths to it."

I was expecting a few iterations of a fractal, just enough to make the boundary of the hole be larger than the largest circumference of the pumpkin

That second pumpkin was a parker square moment. But we love you for that

I was expecting you to cut out a quite thin band of pumpkin along a similar line as the line on a tennis ball, which would've allowed you to pass the original pumpkin through this band, if you stretched the band into a full circle, which would've been bigger than the original pumpkin.

The thing is though, it's really easy for the hole to be bigger than the pumpkin if you're thinking of the size of the hole being the total removed volume, and the size of the pumpkin being the resulting area of pumpkin matter.

Brought back memories of a book read long long ago, in the days of my youth (sorry Led Zep), which featured an item on how to pass a cube through another cube the same size. Thank you Martin Gardner for providing so many things which made me think, and aided the development of lateral and rational thinking. I

My brain enough with prince rupert's drop, now its time for prince rupert's cube to shine

sadly, I would've loved to see the 'bigger' pumpkin through the 'smaller' pumpkin. close approximation in size isn't the same

Matt has succeeded in using maths to make probably one of the most gruesome pumpkins.

The whole time I was just waiting for Matt to discuss the napkin ring hypothesis since he was taking circumferential cross sections!

there's so many puns and dirty jokes that can be used here

What a hole-some video! I was hole-ly impressed by the amount of effort you put in. Happy Hole-oween! I'm just digging myself into a hole here. I'll see myself out.

I mean, it depends how you define "bigger than". Personally as a 3 spatial dimensional being I am under the belief that volume is size, not area. Of course you could define a hole as the cross sectional area of an enclosed through-termination of material, but I would consider a hole the volume of said termination. However, ignoring my pedantics, this is very interesting.

This really boils down to "can you fit the smallest profile of something through its largest profile" which doesn't really need investigating, it's obvious.

If you put the original pumpkin closer to you, and carve the hole further away, it's a lot easier to do because the perspective makes it smaller.

When you do the final demonstration with the octahedron, it takes you a bit to get it through even after you get the right angle because we are human and don't think or move in perfectly straight lines perpendicular to a particular cross section. Does rotating the octahedron passing through the hole change the minimum size of the hole?

Cutting such a large hole in the pumpkin would surely leave it gourd

This IS interesting, but my issue with it is that the question is so ambiguous that the thing you ended up demonstrating was not how I would interpret the original question, mainly what "bigger" means in the question. 'Cause like, say I take your pumpkin band and try to fit an identical pumpkin through in the SAME orientation. That's more what I was thinking, because what you're actually showing is that different cross sections have different dimensions, not that you can make someTHING bigger than THAT thing started (the originally oriented pumpkin cross-section). In that way, it's kind of a bait and switch in terms of what "it" is referring to, from MY perspective on the original question at least. I think of the two cross sections as different things. Semantics are often underestimated - they impact conceptualization. I think the thing you're talking about IS important and significant in math, I DO get that impression as a layperson, I just think it's not quite the thing you're framing it as conceptually. It's not really about 'a thing being bigger than it started', it's more about the geometric relationship between shapes based on orientation. That's what I take away from the actual information in the video.

-My hole is so big it can fit 2 cucumbers-

The answer: depends on the thing

wait, the spooky halloween mix of the theme music is actually awesome!

Yes, you can cut a sheet of a4 paper in such a way that it makes a big loop

Student: Why would you need all this complicated maths in life? Matt: Hold my pumpkin..

This is made to be much more complicated than it actually is! A square prism that measures 1x5x10 will have one profile that is 1x5 and another that is 5x10. It would be a trivial task to cut a 1x5 window into the 5x10 face, that's kinda' how windows generally work anyway... a little too much drama me thinks..

2 days later and I'm hooked on the podcast!

this is cool, you're saying i can take cube A and fit cube B which is 6% bigger inside it. Can i then take these interlocked cubes and put cube C, which is 6% bigger than cube B inside them too? What would that even look like and could i just keep putting larger cubes inside each other?

That he didn't refer to the 2nd pumpkin as the "stunt pumpkin" will haunt me to my grave.

this is so awesome. Matt, you legend, i have mental health issues and your videos have helped inspire me to go back to university. i dont care if i fail. giving it a crack mate.

5:18 "If the pumpkin don't fit, you must acquit."

🥟

Last time you did a hole video I ended up wearing a torus instead of trousers. I was four hours in the emergency room screaming BUT THEY'RE TOPOGRAPHICALLY EQUIVALENT

I first heard this topic on the podcast, and I'm pretty amazed the 3D model I created in my mind based on Matt's explanation was exactly what the video showed! That was some impressive describing on his part. Very cool to see the actual pumpkin being referenced though.

12:00 so THATS what the kids toy where we have to fit the square peg in the square hole was training us for!

I just learned that a 4D cube (or any even Detentioned shape) can rotate without an axis of rotation. This is because when finding the bull space determinant (how you find the eigenvectors of which an axis if rotation is one) you're actually looking for the zeros of an n dimensional polynomial where n is the dimension if the matrix. And any polynomial where the highest degree is even, doesn't need to cross the x axis.

I think for this one, you get a definitive DING!

There is far less Banach-Tarski in this video than I expected !

Matt: I can carve a hole bigger than the original pumpkin. Topologist: No matter how big or small I cut it, the hole will always be the same size as the pumpkin

Okay. So at 5:30 who else was like: "Put it on your head. Come on. Do it. Why don't you put it on your head?? PUT IT ON YOUR HEAAAAADDDDD!!!" xD

Matt: A Jack o' Band-tern Me: A Parker Pumpkin

I don't like Halloween, but i like this

[Calls up the 1600s] "Hello, do you have Prince Rupert in a cross section of himself?" [The 1600s]: ಠ~ಠ

Holey pumpkins, batman!

This video is crazy. Particularly the moment when the second pumpkin appears and is declared identical to the first pumpkin without any further explanation.

I never knew about a problem squared untill now, it's amazing I just binged listed most of it

I mean, it seems pretty intuitive that if you take something with different profiles (like the 1x4x9 monolith from 2001: A Space Odyssey), and chop a 1x4 hole in the 3x9 face, it's going to fit through itself easy-peasy.

Came here from the podcast, and whilst I think this is an excellent video/maths journey, I do agree with some posters that the definition of "bigger" is quite loose here. If you cut a small slot in a surfboard and passed another surfboard through it, would you say the slot it "bigger" than the surfboard? Not really. But it's still cool, keep up the good work on all fronts!

This is like the making a hole in a regular sheet of paper big enough to walk through.

4:25 ".... And by the power of buying two of them..." Tecnology connections would be proud

I love the Halloween remix of your normal song

"Good enough, is close enough" should be in the channel description.

Imagine listening this out of context "Today we are going to find out: How big is the whole in your pumpkin?" "How big could that hole be?"

"This is how the sky looks like in England in October" Me, seeing no rain: "Is this CGIed or something...?!" 😅

7:19 "leaving pumpkin behind". I see what you did there

I think that crossection juggling is more of a stretch than stretching/distorting the pumpkin.

8:10 it was the same Prince Rupert that got stressed over a fragile drop of glass!

Thanks, now I can fit a pumpkin inside a smaller pumpkin!

Love the what we do in the shadows reference

I'ld wish you would also make two spiral cuts winding around the pumpkin from top to bottom and unwounded it into a giant hoop you could probably step through.

Nice bonus at the end of pumpkin part))

Always excited for Halloween episodes!

This Prince Rupert was good at getting things named after him. The eponymous drop. The eponymous cube. Any others?

"It's a success!" we have made a smaller pumpkin fit through a slightly larger pumpkin... we did it folks.

when i read that title i was reminded of the old parlour trick of stepping through a postcard. the trick is all in the cutting, and i am right