Topology of a Twisted Torus - Numberphile
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- Опубліковано 19 чер 2024
- Featuring Professor Carlo Séquin - see more from him at: bit.ly/carlosequin
More links & stuff in full description below ↓↓↓
More on this topic soon...
Animation by Pete McPartlan: bit.ly/PeteMcPartlan
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Frankly I'm impressed he was able to cut the bagel like that
I know right
Math gives you super powers dog
"I'm Carlo Séquin and this a bagel"
+David Joffe-Hunter One of my favourite Numberphile quotes. The bit at the beginning about the Galactic Concentrator is also one of my favourites. XD
XD
The bagel
What is your Erdos number and n0mn0mn0m :-)
( :
Ah, mathematicians. Figuring out the best ways to cut bagels.
I like your profile picture
he is not a mathematician he is a computer scientist
Nice profile picture
@@scienceium5233 not far off.
@@scienceium5233 a computer scientist IS a mathematician. You are thinking of software developers.
"You can put MORE Cream cheese in this bagel!"
The excitement was palpable lol. As was my amusement.
I'm REALLY tempted to try this... even better would be to request a Noah's bagels to cut their bagels like this and then just explain to them matter-of-factly: "I'm a commuter, I need my bagels cut this way" and just show them the screencap of him holding the bagel-chain :P
Has been years
Did u do it?
We need answers
What? No lox?!
"What's a Mobius Band you say? Well I'll show you."
*zzzziiip*
Wow
@@flashbacktim Wow indeed
@@BearsThatCare Mathematicians get really excited about Mobious strips, don't they?
@@Jonassoe They really do
I used to hate maths before I started watching numberphile; now I'm working my way through Martin Gardner puzzles and studying high order logics! Thanks for giving me the kick I needed!
thats great to hear i'm really glad these get really sucked into learning dont they?
i use HATE learning anything til starting watching these helpful vidoes
I'm gonna build a mobius house, then my mum can't hassle me about spending too much time inside.
I think you mean Klein house.
But what if it rains?
it will rain on the out... wait... hmmm ... let me think about that
@@Chigger Then the house should be designed to channel the rain flow away from the stuff you don't want wet.
Thanks or all the great comments - animations were done by a chap named Pete McPartlan
I would really like to hear more from Carlo Séquin. As a student of electrical engineering, I've heard his name in a class I'm taking where we learned to program a RISC processor (NIOS II on an Altera DE0 board). You should invite him to talk about RISC on Computerphile; it's a significant development in computer engineering that I think viewers would take an interest in. I think he also did some interesting things with SPICE and graphics, but I can't recall. TL;DR: I'd like to hear more from this guy!
Those were some pretty awesome animations. They had a kind of early 3D video game vibe to them, like something you'd see on the Atari Jaguar or Sega 32x.
I want to take what this guy takes :))))
Mes hommages à M. McPartlan. Très Impressionnant!
***** I don't get why these numbers and their theory matters. It all sounds abstract and without any real life application.
thank god. I knew I wasn't getting maximum cream cheese on my bagels. XD
+David Crawford Not only can you get maximum cream cheese, you also can have a bagel that won't drop if one of the halves slips out of your hands! It's the ideal bagel! Aside from how labour-intensive it is to prepare, of course. XD
"You have been eatin' bagelz wrong!"
+Awsomiihill every buzzfeed video, lol
When maths is involved, somewhere along the line the cream cheese becomes infinite.
David Crawford have you tried deep frying the bagel in cream cheese?
9:30 - You're having far too much fun with these animations, aren't you Brady? :P
Just like a mobius strip this video started and ended with the same scene and words.
Better if it had ended upside down. :)
I want to find someone who talks about me like Carlo Séquin talks about cream cheese
Ooh, horny
I'm always impressed by the animations in your videos.
Thanks - the animations in this video were created by our good (and talented) friend Pete McPartlan
why?
Because it isn't easy to animate such complex shapes and they invariably illustrate the points being made very clearly.
Numberphile I've seen more of these animations in newer videos. It's a great addition and very well done.
Thank you!
Great person to have on Numberphile, obviously passionate about mathematics while maintaining a childlike wonder for the strange properties it produces, as well as being a funny guy to boot. More with him, please.
Yes, i agree. I also think he is a vampire.
I love how excited this guy is about cream cheese.
This is now how I apply cream cheese to bagels. Double torus or bust.
u mean everybody isnt that excited?
ShadowDragon I hat cream cheese...
Great video! Great animation Pete!
Am I the only one really bothered by those crumbs falling onto the floor?
Because I don't let my food fall all over the floor?
*****
In that case, the difference is in our opinions.
To me it seems to be a lot.
+Isaiah Kilgo Do you want ants? Because that's how you get ants!
Isaiah Kilgo how big is your floor? It's understandable if you have a small one but if you have a large floor you wouldn't notice the crumbs...
Choose Vanu. Choose Enlightenment.
I like this guy
i'm just gonna say..leonard nemoy
Brilliant, this guy is amazing
08:48
Professor: A mobius band!
Brady: Ah! :D
Professor: What's a mobius band? Lets see!
Brady: Oh D:
Haven't had a bagel in years.... Now gagging for Philadelphia cheese and a torus made of dough.
Philadelphia jalapeño cream cheese on an onion bagel bro. Tops.
I really want a model of that triple-twisty torus.
Am I the only one who thinks these things are absolutely beautiful, and am wondering where to buy one?
You would probably have to 3D print your own
I was thinking the same thing, and I was hoping that there would be more presice hits on Shapeways.com, but no luck yet though. Maybe Carlo could release the 3D files in someway, so somebody with the 3D Printing knowledge and know how can put them on Shapeways? :) That would be really cool :)
some people dont have 3d printers though...lol
they just look so...good. Escpecially the ones that only go 180
I don't have one my self, that's why I thought it would be great to put it on Shapeways, so they can print it, and send it to you :)
Ah
why is this so exciting? seriously i am like crazy amounts of excited about this!
I think this guy is my new favorite. He's a tremendous talker, he perfectly manages to maintain interest in himself and somehow not for one second bore you. Splendid choice, Brady.
"What's a mobias band? lets find out."
Numberfile XXX
I love that he actually had all the different objects instead of just talking about them in theory. Maybe this is something for Maths Gear?
Yay for topology!
Fantastic Video as always. Those 3D printed models were very impressive.Those guys must have a really nice printer to be able to make shapes like that so perfectly.
He's getting crumbs everywhere!
Yeah :D some people just can't be bothered to be bothered. If it makes sense...
"takes of belt"
Brady: Ohh
This was interesting! I hope we will see more of this amazing man.
7:20 Aaaaaaaand it looks like an onion.
Topology really is the most mind blowing, make a lot of these please
Mobius houses. This pleases me.
No bagels were harmed during this video T-T
+Abdulrahman Majash On the contrary; many were vivisected.
Putting it perfect back together without even looking
Look at the bagel at the table at 2:26
This is so fascinating! Thanks for making these vids, Brady :)
A bagel is made by joining the two ends of a tube of dough.
If you put two tubes alongside each other, twist them and join the end of one to the end of the other then you get one continuous piece of dough, the same result as Carlo gets when he cuts a bagel while rotating the knife only 180 degrees (at 7.36 in the vid).
If you do a double twist and join each tube to its own end rather than that of the other you get what Carlo gets earlier on (1:33) when he rotates the knife 360 degrees, the two tubes are separate pieces of dough but chain-linked.
You know, I have a feeling if all math teachers were like this guy people would be a lot more interested in it. XD
+Jon Don Von Bonbon That's because he is only talking about the not practical or applicable part of math, meaning less equations and statistics.
Fair enough
+Jon Don Von Bonbon I love learning about topology, but have you seen the notation? At some point you have to get into the notation and I haven't got my head round that yet.
Potentially one of the best numberphile videos ever. Now I know how to get the most spread on my bagels
Can you guys do a video on Gabriel's Horn (a.k.a Torricelli's Trumpet)? For those who do not know, it is a solid with infinite surface area, but a finite volume. You can get this solid by taking the function 1/x for x >= 1, and then rotating the entire function on the domain [1,infinity] about the x-axis.
There's a video titled "Infinity Paradoxes" that talks about it.
***** Thanks. I have since realized that.
1 question: what if I filled it up with paint?
Not bad
Devin Allen That's the paradox.
Numberphile has gone into topology! YAY!
awesome video and topic Brady! Prof Carlo Sequin was awesome, please do more videos with him!!
I'll make myself a few of these things as soon as someone in my vicinity gets a 3D Printer :D
Good stuff. Any chance of doing something on 4D polytopes?
To be honest, most n-dimensional geometry/topology is FASCINATING, and doesn't require a lot of prior knowledge or arithmetic to explain. I'm surprised none of the videocaters are really going into it.
D. Tysen Well, let's get the hyperspere ball rolling! Especially in higher-dimensional spaces... :)
@@SOBIESKI_freedom What's cool is that these very same people made a video on 4D polytopes/polychora.
your joke about the 'galactic concentrator' at the end just gave me a crazy idea lol
I keep coming back to the video. I think it's the combination of Prof Sequin's calming voice and something satisfying about the 3D models
Amazing teacher :-)
I really want a bagel now.
Stuff like THIS is why I love this channel so much! Thank you!
Fantastic, Brady! you've outdone yourself with this one mate! And more to come I see, can't wait.
How did you get that three-way knife inside the torus in the first place?
Theoretically! :) I believe that to make that actual shape though, he 3D printed it with a spacer that he removed so that there would be a break in the torus.
Didn't you know? All bagels have an optional 3-way knife cooked into them.
Manabender you can insert 3 blades separately
Manabender He said made it them using a modeling machine, so i guess its made slightly differently than how it shown.
Manabender you could make the blades detachable so you mate a slit to put one of the blades in and then put the other one in and attach it again
I have to say that I love the animations. Especially the one at 9:31 where you keep displaying the strip as being a belt. Makes it a lot more clear :)
Great video.
Ya, they where very well done.
Brady, this is probably one of my favorite numberphile videos. Thanks so much mate !
This is why you subscribe to any of Bradys channels, you never know what to expect and he always seems to find interesting topic.
Those models look like they're 3D printed, right? (Besides the bagel, of course!) :P It would be the most awesome thing ever if your team could post the CAD files for them!
Fdm printed
Professor is great and interesting. Hoping for more videos with him.
his talks and models are amazing. love it. post more please
Great interview and clear animations -- thank you!
I would love to see the shape of a 720 degree cut. Clearly you will get 2 pieces, but what do they look like and how do they hang together? Could this possibly be a follow up video?
So much cream cheese.... I want that bagel. This information shall be invaluable for the bakers of the future.
New York's Famous Torus Bagels!
Beautiful video. Loved it. Cant wait to see more.
Thoroughly enjoyed this! Can't wait for more.
I already wanted to write a comment saying that it really reminded me of the Möbius band halfway through the video, and then, there it is! :)
Wait a minute... Your not suppose to be eating a bagel dry? *mind blown*
No, you monster
This was great, and the animations helped a lot!
Very interesting video and beautiful forms he have there! Mr. Séquin looks like the kind of guy that you can talk for hours and hours without getting bored. I would appreciate a continuation! cheers from Brazil
You had me at more cream cheese.
Professor Carlo Séquin is awesome, can't wait for more cool topology videos with him :3
I love this guy. I think this was one of the most entertaining and informative numberphile videos yet.
This guy's voice is incredible.
10:40 The Galactic Concentrater. I've gotta say, I'm kinda curious as to what the "right spot" entails.
I really enjoyed this video! The topic is fascinating and Professor Séquin is wonderful. I'm sure I'm not alone in hoping to see other videos like this in the future.
i love the animation in this video. great work!
Who had the awful job of CADing these for the 3D printer?
Probably Séquin himself haha. And I bet they're pretty easy to make in something like Openscad where you can define surfaces parametrically.
Carlo Sequin is a computer scientist famous for pioneering a lot of modern computer graphics and CAD software... so yeah, he probably did it himself
I like your profile picture.
Infinite blades? INFINITE CREAM CHEESE!!!
I can't wait for the next one. So great.
I didn't expect to see any topology on numberphile: it's a welcome diversion from the usual focus on natural numbers, especially with such cool constructions!
Now I want a Bagel, with topologically efficient cream cheese filling. Damn you Carlo!
Great production and a fascinating topic. Topology has always seemed like an intriguing field to me.
Can't wait to see more!! So cool!!
This was awesome! Looking forward to the sequel!
Reminds me of the Samus's Morph Ball.
I love this guy haha:D
Brilliant video and amazing animations to illustrate the cuts.
Amazing geometrical spaces from cutting a torus in different ways. Beautiful!
i never ate a bagle in my whole life
Put it on your bucket list! You can add some butter and delicious ham to make it even better! :3
What about a bagel?
You're probably right, since you can't even spell it :)
you’re missing out
We dont have bagels in Italy
Can't wait for the Möbius houses
Professor Carlo Sequin seems like a really interesting person with loads of interesting knowledge to share. If ever he has time and a topic for an interview, you shouldn't hesitate.
I love how the cameraman is always learning something and is amazed
Oh my God. More like this please. :P
"And what's a mobius band?"
?
What?
Wait.
Wait...
Wait!
WAITWAITWAITWAITWAITWAITWAITWAITWAITWAITohhhhhhhh.
Amazing! This is really fascinating!
If you do that last cut on an inner tube, you get a continuous strip of rubber with a knot in it! (source: Martin Gardner)
The 540-degree spiral cut? (a.k.a. the "Galactic Concentrator")
*****
I meant the cut illustrated at 09:43 in the video. I'm not really a fan of fanciful names like the one you mention. :)
JimFC Gregg Yeah, that's what I meant.
The Galactic Concentrator, lol :) :)
Gosh this guy is great :)
This is awesome! A very inspiring video!
A Mathematician Baker suddenly gets the idea to cut a donut into twelve pieces using this technique and calls it the dozen in one donut.
Dammit, now I accidentally dropped my klein bottle.
Oh, no! I hope all the liquid didn't spill in!
is there anywhere we can buy these torus shapes? Such beautiful pieces of art.
Your nearest bakery?