Can you make a hole in a thing bigger than the thing?
ฝัง
- เผยแพร่เมื่อ 30 ต.ค. 2021
- Listen to my podcast A Problem Squared! aproblemsquared.libsyn.com/
This is Bec Hill.
/ @bechillcomedian
www.bechillcomedian.com/
Huge thanks to Sam Hartburn! Check out her posts on 'Rupert Polyhedra'.
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Filming and editing by Matt Parker
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MATT PARKER: Stand-up Mathematician
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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!
It's the funniest podcast I listen to I think.
DING!
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.
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.
True, but A Problem Squirrel is much more dramatic.
Do that with a sphere and I'll really be impressed.
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
A Parker Sphere Hole would be nice.
Start by assuming that a cube is a close approximation of a sphere
I bet you could do it in higher dimensions
@@vipsylar6370 They are called good enough spheroids.
Depends on how you define "the thing", "hole", and "size".
Yeah this isn't so much a mind-blowing trick as it is a matter of definition.
Also "can", "you", and "make"
Okay, Bill Clinton.
@@chitlitlah It's 100% true and fair though, and I personally don't interpret the question the way Matt answered it. From my comment above about how I interpreted things:
"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."
Don't those seem like completely distinct concepts to you? Because they do to me, which is why the ambiguity the OP is talking about can actually be an issue. To me, the "thing", the "it" in question would be A cross-section, so what Matt showed would be two different "things", and showing that two different things are different is less mind-blowing than that one thing can be somehow made different enough to have different properties while still being the same "thing". THAT sounds impossible to me, and as far as I know it is - Matt didn't address that question.
How many cubic inches is the surface of 2 inch radius circle.
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.
Or even a topological trickery such as the one that says that a balloon has -1 holes.
@@olmostgudinaf8100 A balloon has 0 holes, because the knot at the end still has a hole through it, however small it may be :)
Like how you can peel an orange in a spiral and make it into an infinitely long piece.
yeah, like the trick i learned as a kid to climb through an a4 sheet of paper
You can do something like that with a sheet of paper. Its fun to bet people you can cut a hole in the paper that you can fit your whole body through.
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
Yeah, honestly, this concept becomes a whole lot simpler when you think of shapes with less symmetrical geometries
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.
@@mmseng2 I’m a big nerd, so my first visualization was literally just 2 identical rectangular prism
@@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.
@@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
That settles it, I'm putting pumpkin scraps on my front porch and calling it the 'Parker Pumpkin' AKA Matt-O-Lantern.
Why does this comment not have more likes??????
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.
😂
Why not just the card board projection haha
That's so Parker-ish!
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!
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.
@@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.
4:18 you missed an opportunity to say "with the power of buying two" and connect with Technology Connection channel
through the magic of buying two!
“And, through the magic of buying two of them, I have an already taken apart one for us to examine!”
Since it's "a problem squared" surely it's "to the power of two of them"
I’ve always heard this is why man-hole covers are circles instead of squares. Otherwise, the cover could fall into the hole.
But not all manhole covers are circles. I believe the boring truth is that manhole covers are usually circular because most manholes are round.
Don't they just have a lip?
@@ryleighs9575 Yes. Point is a square hole, even with a lip, is big enough for the square cover to fall into.
@@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.
@@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).
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.
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).
I agree, I feel swindled
I Think The Same, It Feels Unintentional Clickbaity
@@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?
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.
Matt proves in math, that a couch, can fit through a door way. Essentially
Or that a door can fit through a doorway.
This is like the adult version of those kid "puzzle" toys where you have to fit the shape through the right hole.
This explains how everything is able to fit in the square hole
@@adamx9065 The...the arch! The arch! *face of absolute betrayal*
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.
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.
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.
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!
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.
nah, it's not the only shape. there's a family of shapes called curves of constant width
They aren't circles
It's the easiest shape to manufacture that can't fall thru itself, although others exist
ahh.. the ever popular.. visual demonstration on a podcast.. brilliantly done Mr Maths. Or can I call you Stand-up?
I'll take "jokes that don't work on the radio" for 300, Alex.
R.I.P, Alex.
cutting a hole in a sphere wouldn't work , correct?
because it's projection is the same no matter the angle.
@@PeppoMusic A sphere is already by definition the ("zero thickness") surface of a ball.
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?
Yes, but the question is, is the sphere the only body it doesn't work?
@@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
@@PeppoMusic I'm fact i don't think its possible on any shape with an axis of symmetry.
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.
Well, the first five minutes were definitely a parker square of an answer.
So it's a Parker answer. I do'n't know what else you'd expect.
Well the "duplicate pumpkin" was certainly a Parker duplicate in every sense of the term.
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.
Thank you!
There may be a hole of love in our lifes😔
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.
I'm pretty sure you could mathematically cut out an infinite area of the pumpkin with some kind of fractal pattern.
@@Ghi102 you cut out a fractal with an infinitely long edge, but not an infinitely large area out of a finite 2d curve. Fractals cannot magically add space, they can only make it more complex.
@@Ghi102 Nope, that's just not how fractals work. You cannot rearrange a finite area into an infinite area, no matter what you do. That is, if you only count the outer surface of the pumpkin. If you're fine with scraping off increasingly thinner layers off of the shell, perhaps leaving a small connection so it's still one whole, then fold all of that into something flat, then yes, you can turn that finite *volume* into an infinite area. That's the magic trick behind all those fractals, they take a finite entity of some number of dimensions, and turn it into an infinite entity that has at least one dimension less (volume to area, area to line, etc.)
@@Felixr2 Technically, what you're saying is true only for finitely many cuts. Otherwise I could invoke Banach-Tarski to turn one pumpkin into 2, thereby doubling the surface area.
Hi Derrick!
I'm loving all the remixes of the theme song recently.
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.
But can you cut out a human sized hole out of a human, to fit the original human through?
@@AFAndersen easily. smallest cross section would be top down and would easily fit through the largest cross section, facing forward. could probably fit at least 2 or 3 copies of one human through itself at the same time
the taller and slimmer the person, the more you'd be able to fit.
@@daniellebarker7205 i suppose the inherent gore of the solution is appropriate for the holiday... 😬
@@AFAndersen - Most humans come out of a hole in another human, so that sounds mathematically possible. Might require time travel to make it the _same_ human, though.
"This is what the sun looks like in England in October"
imagine being in October for ever
That's Manchester
I wouldn't mind. No heat waves, no extreme cold. Trees look stunningly beautiful, and interesting math videos show up. 😃
october forever, so north england/scotland
Imagine being at the Costa del Sol forever.
@@_John_Sean_Walker ill take permanent autumn thanks lol
This is essentially the inverse of the manhole cover problem.
What shape can you use to never drop the lid down the hole?
Any polygon other than a circle has at least one orientation that can fit into the hole. With a wide enough lip, you can use many-sided polygons; the wider the lip the fewer sides you can get away with. If you go beyond polygons, a Reuleaux triangle also works, because like a circle it has constant width.
If you allow weirder shapes, I think certain hypocycloids would work. Feel free to figure out which ones do and don't.
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 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.
So a sphere I guess is the worst-case scenario with zero clearance?
It's impossible for a sphere. For it to fit, you need to cut the whole with the diameter of the sphere, which will remove evrrythig.
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
Me too
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
Yes, 😃👍
Same thing with aircraft doors, where the 'plug' is bigger than the hole, and requires a twist to close.
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!)
I was always told that it was so they couldn't fall in
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 : )
That second pumpkin was a parker square moment. But we love you for that
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
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.
His last "Hole....ly" video was about how many holes a balloon has.
Always excited for Halloween episodes!
"What happened to Matt's pumpkin?"
"He did maths to it."
"Same size cube, that's actually a bit smaller, fits right through itself." Who would have thought. ;)
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.
So many videos lately! love it
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
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
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
@@squorsh 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.
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
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?
Not sure about the octahedron but it definitely does for some shapes; imagine two pieces of elbow macaroni.
Rotating something changing the minimum size of the hole is basically the entire principle that a screw is based off of isn't it?
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.
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!
The whole time I was just waiting for Matt to discuss the napkin ring hypothesis since he was taking circumferential cross sections!
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.
In that case hole volumes larger than container volumes are trivial - most containers/pipes enclose more volume than the material of the container/pipe. I'd argue area and length to be more interesting.
2 days later and I'm hooked on the podcast!
Matt I love your videos. I studied math in college but I don’t think I learned nearly as much from that than what I learn from your videos.
sadly, I would've loved to see the 'bigger' pumpkin through the 'smaller' pumpkin. close approximation in size isn't the same
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.
I never knew about a problem squared untill now, it's amazing I just binged listed most of it
Matt has succeeded in using maths to make probably one of the most gruesome pumpkins.
The answer: depends on the thing
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.
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.
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.
@@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.
@@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).
My brain enough with prince rupert's drop, now its time for prince rupert's cube to shine
there's so many puns and dirty jokes that can be used here
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?
Ooh, you could get some cool effects with nesting cubes...
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..
I was thinking the same thing. It would be a 10 second video.
yes because people like you dont enjoy having fun, where as the rest of us do and enjoyed the video for the seasonal bit of fun it was. Maybe you should go read a text book, it may be more your speed.
Instant like on your video after hearing the first few notes of your theme song in a Halloween vibe 😁
Oh wow, just finished a problem squared and saw this in my feed. Fun timing! Love the podcast. Nupboard by the way
Yes, you can cut a sheet of a4 paper in such a way that it makes a big loop
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.
Hell yes. If you can do it, maybe I can.
-My hole is so big it can fit 2 cucumbers-
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 just listened to the podcast, just to find a video of you showing the results!
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.
Student: Why would you need all this complicated maths in life?
Matt: Hold my pumpkin..
As always, the legend that is Matt's theme music person knocks it out the park. Is there another channel out there with so many variations of theme?
wait, the spooky halloween mix of the theme music is actually awesome!
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
Nice bonus at the end of pumpkin part))
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
Loving the Halloween version of your theme song
There is far less Banach-Tarski in this video than I expected !
Cutting such a large hole in the pumpkin would surely leave it gourd
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.
Thanks Mr Parker! You’re the best.
This was a fun maths video. Thank you.
That he didn't refer to the 2nd pumpkin as the "stunt pumpkin" will haunt me to my grave.
I love how the more you look into maths the more you fine answers of "Yes, as long as you ignore [insert stuff to make the answer yes]" @3:09 lol Another way to phrase that is 'We can cut a hole bigger then the object. If we ignore the actual area of the missing elements of the object, that is the area of the hole." or the 'size' of the hole :P
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
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 think for this one, you get a definitive DING!
I don't like Halloween, but i like this
Huge fan of A Problem Squared, 10/10
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.
Happy Halloween!
5:18 "If the pumpkin don't fit, you must acquit."
Matt: A Jack o' Band-tern
Me: A Parker Pumpkin
[Calls up the 1600s] "Hello, do you have Prince Rupert in a cross section of himself?"
[The 1600s]: ಠ~ಠ
I love the Halloween remix of your normal song
Love the what we do in the shadows reference
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?"
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.
It works for all five platonic solids. They all have the Rupert property.
This video is crazy. Particularly the moment when the second pumpkin appears and is declared identical to the first pumpkin without any further explanation.