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

This is Bec Hill.

Huge thanks to Sam Hartburn! Check out her posts on 'Rupert Polyhedra'.

Prince Rupert's Cube on Mathworld.

My previous Halloween videos:

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

[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!

[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

[QuantumHistorian]

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.

[NatePrawdzik]

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

[Pinocchio]

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

[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!

[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.

[rustymustard]

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

[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.

[DaveBermanKeys]

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

[TheViolaBuddy]

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.

[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.

[NoNameAtAll]

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

[MegaJohnny]

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

[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.

[stapler]

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

[rothreviews]

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.

[razielhamalakh]

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!

[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.

[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.