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The Napkin Ring Problem


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Published: 1 month ago
Brain Candy Live FALL TOUR: http://www.braincandylive.com/tickets
The Curiosity Box: https://www.curiositybox.com/
LINKS TO LEARN MORE BELOW!

my twitter: http://www.twitter.com/tweetsauce

Adam and I (but mainly Adam) making a kendama: https://www.youtube.com/watch?v=i8GD33DsRw8

Orange Oil: https://en.wikipedia.org/wiki/Orange_oil

Napkin Ring Problem: https://en.wikipedia.org/wiki/Napkin_ring_problem

Cavalieri's Principle:

https://schoolyourself.org/learn/geometry/cavalieri-3d
https://en.wikipedia.org/wiki/Cavalieri%27s_principle
http://www.cut-the-knot.org/Curriculum/Calculus/Cavalieri.shtml

BIG THANKS:

Eric Langlay stayed up all night with me so that this video could come out today. MUCH LOVE https://www.youtube.com/user/ericdraven30

Grant from 3Blue1Brown helped me wrap my head around this topic: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

music by
Jake Chudnow: https://www.youtube.com/user/jakechudnow
and via AudioNetwork: https://www.audionetwork.com


comment  Comments

Sorry Napkinheads, but the solid shown from 0:18 to 0:24 is not a proper mathematical "napkin ring." It shouldn't have flat faces on the top and bottom. That's a mistake I missed in my rush to export this episode before my flight to Montreal this morning :( But I'm glad to be in Montreal! I'm here working on an episode about the power of suggestion ...

1 month ago

500th comment :)

3 days ago

Nice video!

3 days ago

Why do we cringe

21 minutes ago

Orange oil isn't flammable... Citric acid is.

38 minutes ago

This might be too hard but can you do a video on "Can you learn more from the internet, than you can from School"

2 hours ago

Hey Michael, awesome video as always. Really like your channel. Made me much more witty than I was before. Cosmic soul forever. Now I took it from your videos that you read comments on your videos. So, I was wondering if you could make one of the old giant-stars-and-supernovas-and-quasars-and-blazars-spitting vsauce video. Those are the best ones! Age of ancient stars, the black voids, crazy planets, so many awesome topics. Whatever you decide, if you read this, please reply. I want to know if there is a chance of gaining some knowledge about ancient stars in awesome vsauce style! Have a crazy day!

2 hours ago

The universe is a hologram

3 hours ago

this was some intense math!

3 hours ago

"BTW Orange oil is flammable"

4 hours ago

I only watch his videos to come up with some dank ass memes.

4 hours ago

make a vid about tardigrades

5 hours ago

Do you want to see how to make solar eclipse lenses at home with your kids? Look at the video we did with my girls:
https://youtu.be/qCvCwTi3l6Y

5 hours ago

Youtube red ruined this channel.

6 hours ago

H E Y V S U A C E M I C H A E L H E R E

6 hours ago

nigga what

6 hours ago

Thanks for creating VSauce! Your curiosity has been super inspiring.

7 hours ago

Damn Michael 4K?

8 hours ago

And as always, thanks for creating :)

9 hours ago

Hey! I live in Romania...
We do such things when we are in the 6th grade, that means 11yo...

9 hours ago

You know how Michael says, "Hey Vsauce, Michael here," Well I'm trying to figure out, if he's Michael, then who is Vsauce?

10 hours ago

What would happen if there would be no bad bacterias?

10 hours ago

Can you do a video about 42? The meaning of life?

11 hours ago

Hey Vsauce "Is it possible to kill all Jews at once?"

11 hours ago

I'm Black. What's a napkin ring?

12 hours ago

2:25 accidental optical illusion.

12 hours ago

Hey vsauce....
Math here!

14 hours ago

The earth is flat.

16 hours ago

Some people have math allergies. You should warn people about the math content

20 hours ago

Opera logo

20 hours ago

I don't like how your videos are becoming more specialized and less aplicable.

1 day ago

Not applicable to this video, but sometimes when I watch vsauce, I like to pretend that Michael is rapping over his songs

1 day ago

12k people who disliked hates math

1 day ago

That was beautiful

1 day ago

I don't want to sound ridiculous, but I think the demostration is a bit incomplete, I mean, what was shown here is that the area of the ring formed (at a certain hegiht) in a circle by being cut by a cilinder of a given height does not depend on the radious of the circle, I know that by obvious reasons this proves the Cavalieri's principle but I think that in math saying that something is obvious is not enough, you have to demostrate everything, and since the area is not the same as you move in the y axis, I think you would have to use integrals to prove that in fact the volumes are the same, anyway, is just my opinion and sorry for bad english

1 day ago

I was wondering, if you have a PERFECT corner, like, as perfect as it can get, and you walk as far into it as you can, then shrink yourself, and repeat. Wouldn't you be able to continue going into it forever???

1 day ago

Why is there a problem here? Why not just core the tomato the same thickness as the orange peel?

1 day ago

Wow , this was boring.

1 day ago

Oh god ! YOU guys take too much time for one video

1 day ago

has anyone heard of aliens that created humans, and there being evidence of this in a lot of literature. and that theses aliens put gold into their atmosphere to reflect away heat and radiation from there star?
or heard anything about purposeful eruption of volcanos to cool off the planet long enough to counteract global warming?
this is the extent of my knowledge of this stuff, but I had never heard such wild stuff and thought this might be a good place to ask about it

1 day ago

Maaaaaan, I feel stupid after watching this. I love science.

1 day ago

There is an question: what if vacuum(absolutely nothing, no oxygen and chemical elements) is in water- will it make balloon in the water and blop or ot will just be hole in the water- there is a story, I look at Wikipedia and other sites but they have different answers so there are 2 points of look, the vacuum is nothing so it will make hole, but its nothing with NO WEIGHT so it will blop over the water beacuse it have smaller weight. So that is the question. Good video and have a nice day!

1 day ago

1:31
How many people went and produced fuel from oranges? lol

1 day ago

"Let's call this Height: Why." - My thought exactly.

1 day ago

This is confusing and frustrating to understand and I'm not stupid.

1 day ago

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TYPE CTRL ALT DELETE TO SEE THE SECRET MEASSAGE...




cTRL F xd

1 day ago

Ramne Berglund sorry I'm on Android, could you just tell me what it says?

1 day ago

but what determines the percentage of the diameter of the sphere that is cutout of each of the two? it depends upon choosing two subjective measurements for cutout diameter right?

2 days ago

No problem, glad I could be of help.

1 day ago

sargeantsimon1 thank you it was that one bit i was missing! Been bugging me i understand it all now much appreciated

1 day ago

No, you don't cut it out to make it have a specific volume, you cut it out to give it a specific height. Imagine a sphere. It can roll around because it's round on all sides. If you turn it into a napkin ring, it suddenly has a flat side on the top and bottom, because you removed some of the top and the bottom, making it shorter. If you remove a larger portion, it gets even shorter than that.

So say you have one ball the size of a tennis ball and another the size of a soccer ball. You want to turn them into napkin rings with the same height. Let's start with the tennis ball. We'll remove a small core from it, giving us a napkin ring. Now let's remove the same size core from the soccer ball. What happens? The soccer ball doesn't get much shorter at all, certainly not short enough to match the tennis ball. We need to remove a wider core, until the soccer ball's height matches the tennis ball. When the heights match, the volumes are also equal.

Another way to imagine it is like this: imagine you have a lump of clay, and the power to shape it into any napkin ring that could be made with exactly that amount of clay. No more, no less. This lump of clay has its own amount of volume that cannot change even when it is reshaped. Let's start by shaping it into the most compact ring we can: a sphere. Technically a sphere is also a napkin ring, with a core size of zero. This sphere has a certain height. Let's see if we can make a napkin ring that's shorter. We can't just compress it, since then it wouldn't be a sphere or a napkin ring. Maybe we can remove the core, since that makes it shorter, and then add that material back somewhere? But anywhere we add it makes it into a lump that's no longer a napkin ring. Even if we spread that extra clay out over the whole surface, we end up with a shape that's just slightly not a napkin ring. Okay, we can't make a napkin ring that's any shorter, can we make one that's taller? Nope. We need extra material, or else the shape we end up with isn't a napkin ring. But importantly, can we make a different napkin ring of the same height, using the same amount of clay? You bet we can. We can mold the sphere into a shape with a hole in the center, and as long as the shape we end up with is a napkin ring, it will have the same height as the sphere we started with.

That can be a little hard to understand, but it is an interesting phenomenon. Everything he presented in the video is true, except that the shape that you see around 0:18 that stretches out isn't a proper napkin ring because the top and bottom are flat rings instead of sharp edges around the core. This was addressed in a comment.

1 day ago

so basically you have to choose a cutout diameter that allows the volume of the remaining "napkin ring" to equal that of the other ring? therefore this isnt even a phenomenon, and surely the equal height napkin ring of the earths diameter is not equal in volume to the volume of the orange peel napkin ring. I want to fully understand this as it seems this concept is not nearly as captivating as Vsauce tries to make it seem

1 day ago

Whatever portion causes the two rings to have the same height. The larger the cylinder that is removed, the shorter the ring gets.

1 day ago

Somebody please tell me to go to bed I'm dying.

2 days ago

Welp, I just realized I can't math...

2 days ago

lowkey stalls the video to 10 minutes for ad revenue

2 days ago

#FREEJIMMYNEUTRON

2 days ago

Why couldn't you have released this the week before my geometry test???

2 days ago

michael has nice hands.

2 days ago