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

Listen to my podcast A Problem Squared! aproblemsquare...
This is Bec Hill.
/ @bechillcomedian
www.bechillcome...
Huge thanks to Sam Hartburn! Check out her posts on 'Rupert Polyhedra'.
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And here are her files on github: github.com/Sam...
Prince Rupert's Cube on Mathworld.
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My previous Halloween videos:
What is a Vampire Matrix? • What is a Vampire Matrix?
How to make a fold-and-cut bat! • How to make a fold-and...
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CORRECTIONS
- None yet: let me know if you spot any mistakes!
Filming and editing by Matt Parker
Opening titles by Alex Genn-Bash
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
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[@Project_Kritical]

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!

[@gregdesouza17]

It's the funniest podcast I listen to I think.

[@thelastcube.]

DING!

[@LeoStaley]

I still very much prefer a Podcast of Unnecessary Detail. Also has Steve Mould and their friend, and live show collaborator, Helen Arney. But Steve Mould is heckin busy, I reckon, so it's less frequent. Or maybe it's Matt who's too busy because of A Problem Squared, in which case ooooooh, Bec Hill, i am sooo going to turn the volume down a little when you're talking, out of spite. I'll still listen and laugh though so there's that.

[@SaveSoilSaveSoil]

Awesome! I have just exhausted the numberphile podcast and am thinking "what's next". This recommendation is very timely. The universe is a strange place. When I am sleepy, a pillow just falls right into my lap.

[@andyinannarbor]

True, but A Problem Squirrel is much more dramatic.

[@NatePrawdzik]

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

[@veggiet2009]

This reminds me about the 4 circle Venn diagram problem, where the circles symmetry makes it impossible to connect 4 rings together in the correct Venn pattern, yet an ellipse or other shapes is perfectly able to create a correct 4 category diagram

[@vipsylar6370]

A Parker Sphere Hole would be nice.

[@GEM4sta]

Start by assuming that a cube is a close approximation of a sphere

[@pedrofellipe8028]

I bet you could do it in higher dimensions

[@Robert_McGarry_Poems]

@@vipsylar6370 They are called good enough spheroids.

[@QuantumHistorian]

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!

[@ThisIsTheBestAnime]

I think it would be neat to have two metal cubes, one a metal box without a lid, the other a slightly smaller cube with a hole the box can fit through. That way you could pull the holed cube out of a box and then pass the box through the holed cube. It feels like a slightly more dramatic party trick. It might be tough to achieve the tolerances and have still have relatively sturdy cubes, but I think it'd look really cool.

[@idontwantahandlethough]

@@ThisIsTheBestAnime Perfect. If only I hung out with the kind of people who would appreciate neat math tricks. All my friends are morons. Kind morons, but still morons.

[@darcipeeps]

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

[@matthewhubka6350]

Yeah, honestly, this concept becomes a whole lot simpler when you think of shapes with less symmetrical geometries

[@mmseng2]

Indeed. The doorway makes a lot of sense and is much more tangible for the average joe like myself. In my head I originally went with cutting an 8.5" slit in a (US) standard 8.5"x11" sheet of paper, and then just sliding another sheet of paper through it. To make it slightly more theoretically tangible then do it instead with two stacks of like 50 sheets. But at that point, the doorway is an equally good visual.

[@matthewhubka6350]

@@mmseng2 I’m a big nerd, so my first visualization was literally just 2 identical rectangular prism

[@errorlooo8124]

@@matthewhubka6350 Actually that's an interesting point, i wonder if you could measure the "symmetry-ness" of an object by measuring the maximum give/tolerance that a hole which is big enough to fit itself through it would have. For example a sphere would have a give of 0 so very symmetrical where as a cube would have a give of (1-3/4*sqrt(2)) so not as symmetrical.

[@terenzohugel2293]

@@errorlooo8124 That is a cool concept, I'd like to calculate it for a few bodies. Wonder if it's of any use for anything

[@randorandom]

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.

[@aresorum]

😂

[@Dylan-kw8pz]

Why not just the card board projection haha

[@zappababe8577]

That's so Parker-ish!

[@rustymustard7798]

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

[@robertthompson3447]

Why does this comment not have more likes??????

[@NoNameAtAll2]

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

[@wiseSYW]

through the magic of buying two!

[@skippy9214]

“And, through the magic of buying two of them, I have an already taken apart one for us to examine!”

[@SimonBuchanNz]

Since it's "a problem squared" surely it's "to the power of two of them"

[@Viniter]

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.

[@idontwantahandlethough]

That's... not a bad point! Edit: if it was a perfect sphere, this wouldn't work, right? Are there any other shapes it wouldn't work for, or just spheres? I'm guessing it's just spheres, anything else can be oriented to pass through another orientation of itself, I think (or I guess it isn't specifically spheres, just N-spheres of any dimension. Or at least any dimension up to 3, but I imagine it probably follows for higher, although many things don't so I'm not at all confident in that conclusion).

[@Graknorke]

I agree, I feel swindled

[@hank1318]

I Think The Same, It Feels Unintentional Clickbaity

[@arucane8635]

@@idontwantahandlethough what you saying sounds intuitively correct to me but I was thinking. Shape dilations from speeds that are a significant portion of c could allow for a sphere to pass through a sphere right?

[@GummieI]

Yeah, kinda disappointed with this, had expected some messing around with topology. Instead what was shown here seems more like a semantic solution in fact, rather than a mathematical one to me, as such I would rather have expected this maybe from someone like Tom Scott instead.

[@DaveBermanKeys]

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

[@kkobayashi1]

But not all manhole covers are circles. I believe the boring truth is that manhole covers are usually circular because most manholes are round.

[@ryleighs9575]

Don't they just have a lip?

[@Coloneljesus]

@@ryleighs9575 Yes. Point is a square hole, even with a lip, is big enough for the square cover to fall into.

[@Vasharan]

@@Coloneljesus However, most drainage grates are rectangular. Sure, they can probably be manipulated to fall into the hole. But they're square/rectangular because it's easier and cheaper to make a square plate with grates and bars than a round one. Similarly, manholes and manhole covers are probably round because it's the cheapest and easiest shape to make (think how much easier it is to drill or bore a round hole in the road than a square one). The fact that this makes it harder for the covers to fall into the holes is just a fortunate side effect.

[@RFC-3514]

@@Vasharan - The actual holes for manholes aren't made with a _drill._ In fact, they usually start out as a "trench", which is then filled after the shaft has been placed. So making a square hole would be just as easy. The advantage of round lids is that a) they won't fall into the hole, and b) the lid (which is typically thick cast iron and quite heavy) can be rolled by the maintenance crew, instead of dragged. Square manhole covers are sometimes attached to the hole (frame) itself by hinges, so they won't fall into the hole either. Not always, though, some can indeed fall in. Drainage grates tend to stay in place for a long time, and they're not meant to work as "doors" for humans. They're usually rectangular because the narrower they are, the less cars will run directly over them, so making them 60x15 cm is preferable to making them a 34 cm diameter circle (which would have the same total area, but less support in the middle, and would take up more of the road's width).

[@MegaJohnny74]

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

[@Airblader]

@@PeppoMusic A sphere is already by definition the ("zero thickness") surface of a ball.

[@thyrical]

even if it had zero height and thickness though, every point it occupied would also be occupied by the sphere exactly half-way through insertion, and if the objects occupy the same space wouldnt that count as intersection?

[@georgelionon9050]

Yes, but the question is, is the sphere the only body it doesn't work?

[@neiljf1089]

@@PeppoMusic not sure it would work with a spheroid either. For an oblate, the maximum width is the same from any perspective. For a prolate, the same is true of the minimum width

[@neiljf1089]

@@PeppoMusic I'm fact i don't think its possible on any shape with an axis of symmetry.

[@EUPThatsMe]

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.

[@rothreviews2525]

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.

[@clownsforclowningaround]

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.

[@Robert_McGarry_Poems]

Thank you!

[@КлимКроль]

There may be a hole of love in our lifes😔

[@Mister_Ben]

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

[@Felixr2]

So it's a Parker answer. I do'n't know what else you'd expect.

[@MisterUnlikely]

Well the "duplicate pumpkin" was certainly a Parker duplicate in every sense of the term.

[@Azerinth]

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.

[@vsm1456]

nah, it's not the only shape. there's a family of shapes called curves of constant width

[@salerio61]

They aren't circles

[@simon_fox_youtube]

It's the easiest shape to manufacture that can't fall thru itself, although others exist

[@dereknalley]

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.

[@coryman125]

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

[@Autumn_Actually]

I would say that I don't think GLaDOS or Mr. Johnson would be pleased, but they'd probably be happy to watch you meet whatever bizarre geometric fate awaited you.

[@lukostello]

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

[@christopherlawley1842]

Me too

[@Erekose2023]

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

[@posadist681]

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

[@cealvan8941]

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

[@Felixr2]

I can at least confirm that it doesn't work in lower dimensions, because there's no concept of continuous objects with holes in 2d or lower (well, in 2d you can have a hole on the inside of an object, but there's no way for outside 2d objects to pass through that hole without moving in 3d

[@UCXEO5L8xnaMJhtUsuNXhlmQ]

As a layperson it seems to check out. A 4th dimensional object has a 3d projection, and so all you would need is to have two different projections of the object where one is bigger than the other, although I'm having a kinda hard time visualizing what "bigger" means exactly

[@metleon]

@@UCXEO5L8xnaMJhtUsuNXhlmQ Bigger in that case would mean one projection has a larger volume than the other. The way it works for the 3d objects is that you get two 2D projections where one of the projections has a larger area, so going up by one dimension leads to volume.

[@d34d10ck]

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

[@deepqantas]

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.

[@YoshisaurUnderscore]

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.

[@----.__]

Get some help while you're out.

[@robertthompson3447]

His last "Hole....ly" video was about how many holes a balloon has.

[@alveolate]

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

[@ryleighs9575]

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.

[@jamesbelshan8839]

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

[@----.__]

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.

[@DavidGuild]

Well it's not always true for all objects, but it certainly can be. And yes, it's not very interesting when stated the way you did.

[@japanada11]

Not entirely obvious. Just because a cross section has smaller area doesn't automatically make it fit inside of a cross section with larger area. I agree that it isn't surprising, but there's still some checking required - and there are plenty of shapes which can't be passed through themselves, even though the cross sections have different sizes.

[@----.__]

@@japanada11 Fortunately I didn't mention area! I specifically used profile because for a profile to be larger than another it has to be larger in all dimensions meaning the answer is obvious.

[@Felixr2]

@@japanada11 Pretty sure something as simple as a cylinder already makes it impossible. You can't get any orientation that isn't bounded by the diameter.

[@E.T.S.]

@@japanada11 I agree. Take an egg for example. Lay it flat on the table, cut out the typical egg shaped middle section. Another egg with the same size rotated 90 degrees ("Bottom down") would get stuck. Another more diagonal cross section offers more room. The "problem" in this video is something I never thought about in this way, but just for practical reasons I tried to figure out a similar question while moving furniture. Like "Does this bench fit through the door while we have to make a turn to the stairs halfway through." The same happened while we were balancing the same bench on the stairs way up and needed to take a twist. We had plenty of room, we thought, but the needed rotation made the bench "bigger" than it was. We got stuck a couple of times (fingers included).

[@garyhuntress6871]

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

[@darylcheshire1618]

I remember a question from Professor Julius Sumner Miller who asked “why are manhole covers circular?” He quipped the correct answer is not to cover a circular hole. The answer is the circle is the only shape that won’t fall into the circular hole. For example it’s possible to pass a square manhole cover into a square manhole.

[@becomepostal]

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

[@diceblue6817]

perpendicular to the frustum of the prism projected by the maximum cross section.

[@steamer1]

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

[@ratgeyser]

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

[@grinreaperoftrolls7528]

Holey pumpkins, batman!

[@Crunch0r]

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

[@carlthepumpkinman]

6:36 I'd like a crown made of pumpkin

[@Elnadrius]

7:53 Hexagon is the Bestagon

[@markgearing]

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

[@stefanschacht3322]

7:30 Mat does it like steve: little pause, smile, completing the sentence. gorgeous, just need some contact lenses... ha ha happy hallo v33n (;

[@1000dots]

I'm gonna guess this can't work for an icosahedron or dodecahedron, since when you look at either from any angle some of the vertices making up the 'outline' will be behind and some in front of the centre, so any rotation will stretch some parts and shrink others, never all shrink or all stretch.

[@cyclemath]

It works for all five platonic solids. They all have the Rupert property.

[@1000dots]

Matt + a podcast = me subscribing to that podcast

[@nerdsgalore5223]

Always excited for Halloween episodes!

[@jakovsaric9492]

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

[@RoderickEtheria]

Absolutely. Given the size of a card, if you make a hole within that card that falls back and forth upon itself, that hole can easily fit a whole deck of cards within it, and actually, if that's not enough could fit an entire person or more through it. That should suffice to prove that a hole inside an object can be bigger than the object itself.

[@michaelharrison1093]

Watching this video made me think up a completely different math problem that nobody seems to of worked on. This problem relates to flying from point A to point B following a straight geodesic flight path such that your flight takes you across the international date line. Find the longitude and latitude for points A and B such that your flight crosses the international date line the most number of times and that your flight is the shortest distance to cross the date line this number of times. Assume points A and B can be anywhere on the globe - they don't need to be on land. What is the maximum number of times that you can cross the date line and where are points A and B.

[@greenfang9]

I was immediately reminded of the childhood riddle where you cut a "hole" in a piece of paper (A4 or 8.5x11) large enough to jump through by essentially turning all the material into the perimeter. I wonder if pumpkin skin is flexible enough to do that.

[@Robert_McGarry_Poems]

Pumpkin rind hulahoop!

[@flurgerbla7609]

Remember ABCPTTMC! Always Be Cutting Perpendicular To The Maximum Crossection

[@Grim712]

This is very similar to the problem I emailed in. The toddlers block puzzle where they put the correct shape in the correct hole. There is a popular Tiktok where someone, one by one, places each shape through the square hole. My question is, is there a set of prisms and holes that would only have one correct answer each?

[@ltloxa1159]

Finally!!! Experimental proof that things aren't always the same size in every direction!

[@random6033]

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

[@MesaCoast]

There's a grislier solution to this problem Matt-make the border of the hole a zigzag, and cut any nooks and crannies into the outside of the pumpkin necessary to make the remaining shape have a constant thickness. Then stretch it out

[@RFC-3514]

I think the whole point here was that you couldn't _deform_ (stretch or bend) the pumpkin.

[@EnthalpyUplusPV]

Get this man a million subscribers already

[@spiralfractr]

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

[@aarenfiedler]

I was told in highschool (geometry class I assume) that man-hole covers are round because it's the only flat (2d?) shape that can't fit through a same shaped hole smaller than itself.

[@MrJoerT]

2:46 this is going to be a Parker Pumpkin isn't it?

[@sirchuckles8142]

Pumpkin looks like a face when tilted on its side.

[@fernandoschuindt1665]

That melody you created as a "trademark" of you channel is surprinsgly dissonant/unpleasant. LOL However I love everything else in here. :D

[@ZapAndersson]

My OCD exploded at that protective film still on the printer.... AAARRGHHH!!!

[@shermansherbert2570]

Matt, whats the Jurassic park thing on the wall? Looks really cool.

[@TrueEmotionEric]

So, the biggest part of something is bigger than (or equal to) the smallest part of something... what an amazing not at all expected bit of knowledge.

[@klutterkicker]

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

[@christopherbrand5360]

It seems like for Halloween one ought to do that with a person.

[@millwrightrick1]

Anyone who has ever had to move furniture knows that just about anything will fit through its own size hole if you twist if round enough.

[@andrewharrison8436]

I usually find heavy furniture will fit half way through but it is non commutative and the reverse path is not valid.

[@winkworkshop]

Oh wow, just finished a problem squared and saw this in my feed. Fun timing! Love the podcast. Nupboard by the way

[@nahte123]

Why was my first thought, "Of course! It's like how I could a cut a hole through myself big enough for me to crawl through!"?

[@beardwatch1928]

This coul d be the start of something wonderful. I love a new beginning.

[@scottgoodson8295]

Matt and his carboard

[@jimbobbyrnes]

"without collapsing". well there is nothing left to collapse.

[@RobinHagg]

Let me consider a spherical pumpkin in a vacuum,... Oh nooo

[@alainpbat3903]

To accurately measure, I'd recommend applicating this method next year by molding the pumpkin in some silicone and using that silicone mold to create a candy pumpkin and putting the candy pumpkin through the ring.

[@qugart.]

I guess someone is a big fan of Taika. Well, it is a hell of a documentary. BTW everyone saw the uncanny resemblance, too? The 2D-projection just looked like Matt's head's silhouette. Perpendicular.

[@turrboenvy4612]

The cube models are cool, but I need a model of the pumpkin(s)!

[@Wesyan1999]

wouldn't it be simpler to take a picture of the largest cross-section then making a hole in a picture and passing the pumpkin through it?

[@dedwarmo]

Thanks Mr Parker! You’re the best.

[@robertkesselring]

A super simple example would be a 1 by 2 by 3 inch block with one by two hole cut in the two by three side

[@Dalrae]

I thought you were going to measure the pumpkin by it's diameter and then cut the hole in it's circumference! Your way is much better lol

[@devilsadvocate1597]

Never mind the Prince Rupert's cube, I heard a Prince Albert can increase an objects size so it always gets stuck!

[@MrNosterp]

You should do the same thing with eggs for Easter!

[@pysaumont]

Much easier to do with to identical bricks. Put one horizontally and put the second vertically over it. (I agree, though, that cutting the hole in the brick might be difficult, but it works with any rectangular parallelepiped as long as all dimensions are different).

[@MrAllekzander]

This reminds me in a loose sense of the "I bet I can cut a hole in an index card I can fit though" bet.

[@mattgsm]

Could you fit an even bigger object through itself if you can rotate the object while moving through itself?

[@stevenweissenhofer8196]

I approve of this non-consumption use of pumpkin. 🤣

[@abdulahhi]

Matt you made a hole so big it doesn't feel like a hole any more.

[@chrispchips69]

5:35 jack-o-band-tern

[@Badboyrune2k]

Prince Rupert cubes, not to be confused with Prince Albert studs...

[@The1wsx10]

i was prepared for some amazing mathematical insight here...

[@deathsheir2035]

I came because of the title. And my first thought was: YES, of course you can make a hole bigger than the thing itself. It's the same problem of "can you make a hole in a piece of paper, that you can fit through, without ripping the paper?" The trick to that 2D problem, is to fold the paper in half. Your first cut, as close to one of the short sides as possible, and parallel to it (as parallel as you can get), and cut from the crease, to the non-crease side. You do not cut it clean through, you leave a bit of paper left uncut, and that bit of paper you leave, will be how the hole will stay together once it is done. Then you alternate from non-crease to crease, being parallel and as close to the first cut as possible, and once again, leaving a bit of paper uncut, to act as another point for the hole to stay a hole. Continue alternating. The final cut in this pattern, should be close to the other edge that you didn't start from, parallel to it, and crease to non-crease. Then you have one final set of cutting to do... you now cut the paper in half, down the crease, leaving the two end pieces together. Once that is done, open your new hole, and the hole is far larger than the piece of paper you started with. For 3D objects, I bet it'll have to be folded in the fourth dimension or something... Now on to the video to see if I am right.

[@enzoqueijao]

Local man puts pumpkin inside another; calls it math.

[@andreisupervloguri8058]

Really interesting video! Also, at 1:33 Is that a 7x7 Rubik's cube on the shelf?

[@sylowlover]

The most obvious example I can think of is an ellipsoid. Take dimensions 1, 2, and 3, and you have the smallest projection as an ellipse with dimensions 1 and 2 and the largest an ellipse with dimensions 2 and 3. This can clearly fit through the larger protection side with 1/2 units of space in any direction!

[@eirikmellesdal]

Matt are the best Mathlad in the whole ladworld!

[@DavidBeddard]

Very fun, as always! While you technically answered the question, I'm not sure your answer was in the same spirit as the question (no pun intended 👻). Perhaps Steve Mould would be better placed to answer a question about the structural integrity of pumpkins?

[@hillbournesian]

Should have made a gelatin mould of the pumpkin, then you could have passed that through

[@DrJigglebones]

well, clearly, it's a pumpkin napkin ring

[@waltermeerschaert]

You could easily have cut out a shape that allows the pumpkin to hold it's shape but still cut out more than half of the pumpkin's outer shell. How much of the shell could you cut out and have the result still look reasonably like a pumpkin. Stuff Made Here just made a CNC pumpkin carving machine, you could probably borrow it (if you flew to USA).

[@elmaruchiha6641]

Can you make a whole in a marble bigger than the marble?

[@AxGryndr]

You could have gone down a different side of KZbin, figured out, or partnered with someone, to make a silicone mold of the pumpkin. Using the mold, you could have made an exact replica of the original pumpkin. Doing this would have left no doubt that the original would have fit.

[@theEx0du5]

I notice that these all involve projection, which means that the shape does not change orientation when passing through and does not change direction of translation. But I also saw that the octahedron pushed a point through early and may have been able to make some space with some of these changes. Is there work on this problem and whether the constant changes allowing non-projective holes?

[@Ether0]

This pumpkin ring looks like perfect napkin ring which Vsauce desceibed!