Intro to Topology - Turning a Mug Into a Doughnut

How can a doughnut be equivalent to a mug?
CHAPTERS:
00:00 - Turning a Mug into a Doughnut
01:30 - Geometry vs. Topology
02:05 - Review on Polyhedra
02:58 - Euler Characteristic of a Sphere
04:07 - Euler Characteristic of a Torus
04:51 - Euler Characteristic Formula given no. of Holes
05:10 - A Homeomorphism Puzzle
05:42 - Puzzle Solution
06:54 - Topology Complexity Iceberg
07:07 - Closing
Previous Video on Möbius Strip and Klein Bottle: • Paradox of the Möbius ...
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This video is sponsored by Brilliant.

[@SorryBones]

People just can’t wrap their heads around this. I tried explaining this to someone and they told me to get out of their house because they didn’t know who I was. It’s pretty simple if they just watch the video

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Hi andrew, i recently bumped into your channel and i must say i wasn't disappointed. Keep em. coming

[@drewscampfire]

Thanks, will do!

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@@drewscampfire Will you though?🥺 Just saw was quite a gap in your uploads. Which is understandable however considering the beauty of your work, it really is great sir.

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@@c7hu1hu he lied he quit youtube

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[@kjrey9878]

My dude Andrew, I first saw your 4d klein bottle video and instantly subscribed! You're really smart and good at what you do. Please keep creating and I can't wait to see what you come out with next!

[@flyzo1977]

5:42 wow that gave me chills very intersting continue with your videos they deserves so much more views I wish you success

[@hishwaar]

That handcuff puzzle was pretty cool. The 3D animation really helped with understanding. Great video!

[@ShaunakDe]

These animations are amazing!

[@irodionzaytsev]

Mindblowing! Even if you figure out the answer, it is still so incredible to actually watch the deformation!

[@symbolspangaea]

Perfect intro to topology. I've used this one to explain to my wife, why I'm so much time in the computer... Thank you! now she still doesn't understand me completely, but she as a sense of why I like math so much

[@Alexander-xo5ho]

hands down the most interesting video about coffee mugs and donuts ive watched

[@carsonmcnamer5321]

Keep it up man!! You’ll only get better with time. Sorry I’m a little late to this video, had to move into college. Can’t wait for the next video. You deserve way more views with this amount of effort.

[@drewscampfire]

Appreciate it!

[@IAMASTICKSTUPIDPERSON]

@@drewscampfire yea try to post more

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[@hampusbrokmann8249]

​@@drewscampfireyou need to ramp up you video output and you make a ton of money on the side of you normal life. You are way better to show and tell Then most ppl on KZbin, easy to understand and clear pic of what you are talking about. Sorry for the dyslexia hope you understand 😂😂😂👏🇩🇰😇

[@RevShifty]

I hope you're still out there somewhere. Your videos are incredible, and I've already shared a this one and the 4D Klein bottle video a couple times. In any event, I hope you're well. And thank you for these videos, they're incredible.

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This is exactly like that one video where those two people turn a sphere inside out. You’ve earned my subscription.

[@epalios]

I love this channel! You discuss topics im most interested about! Keep posting pls!!

[@nrml76]

More videos on topology for non mathematicians please. You did a great job of presenting concepts in a very understandable way.

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These videos are awesome!!! I’m so glad to have found them and looking forward seeing more. Thank you so much 😊

[@malicksoumare370]

It's exiting how I was glued to the screen even if I didn't learn anything new. Thank you. We are waiting for future videos.

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congratulations on your first sponsor deal, glad your channel is growing and keep it up!

[@cherry1leii]

Damn, Topology is something very different and I kinda begin to love it

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High quality work, really liked your klein bottle video, highly underrated, keep going 👍👍

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I love how I got this into recommendations and I hate how I didn't know about this channel until today

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It's a pity that there aren't any new videos on this wonderful KZbin channel😔

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Dude your videos are incredible, psychedelic even.. The animation is over the top awesome and the music is perfect. You MUST, plz, make more of these 🙏🤘🙌

[@clarenscourtois8927]

That was super great, I can understand 3d and some other things related to complex geometry better now. Thank you!

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[@Life_42]

Beautiful video!

[@father47_]

please continue making videos like this, they are super interesting!

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So many good KZbin channels like this popping up in my recommended section! Keep it up man, your videos are great!

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Just discovered this channel. Really wish to see more!

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This video is great! Definitely deserves more views than just 50k

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omg you have posted again!! i love your channel!

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Excellent way to explanation. Surely you deserved millions of view

[@Swoger]

another really good video from you!

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This is so well done! Amazing!

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Yoo only 4 videos and feels like you are a professional youtuber, you are a great inspiration❤️

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Most mindblowing video I've ever seen

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We need more, keep up the good work

[@nativeantarctican3325]

What software do you use to make your amazing videos?

[@drewscampfire]

I use Blender and Manim! (both are free and open-source)

[@jschmid26]

These animations are amazing, damn

[@BIackhole]

05:10 now way the erik satie's amazing piece, gnossiende no 1 is playing in a video that explains an amazing topic! Two wonderful things together!

[@peterpelle8982]

watching ur animations bring me calm in this hard times of my metal health. THXS

[@srijani332]

Very very helpful... thanks...

[@Dhruva_P_Gowda]

Nice Visualizations!!!

[@hossainahmmed6434]

Keep them coming man

[@igxniisan6996]

If u keep going down in this rabbit hole of topology you'll finally come across with those sphere inside out guys

[@WaleedHassanAwan]

This video was so good ☺️ I loved it so much

[@RSLT]

Interesting. Great video!

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That is absolutely awesome 👌🏻 👏

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This is next level explanations. amazing videos , keep it up. please make videos on fluid mechanics and semiconductor.

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This is one of the best videos i’ve ever watched on youtebe

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Love your vid man keep it up

[@Qlust]

HI, I just wanna say your vidoes are really great and easy to understand!

[@HAG47]

Amazing reall, keep up the good work

[@rasmusvanwerkhoven1962]

So in theory, we could have an object with a negative number of holes, giving it an Euler characteristic greater than 2!- I wonder what that would look like, if it’s even plausible to make. And what about fractions; how would objects appear with a fractional number of holes? Also btw, I loved your video and the neat knowledge it brought!

[@vasil_astrov]

Great video! Thanks! :)

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A sponsorship of a large website with only 4 videos?!?!? This man is insanely good

[@Leo-if5tn]

Awesome video

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Interesting way to expand your mind.

[@aithrasherboi]

I have an easy solution to the straw question at the start of the video, and that's defining what a hole is. Imagine a donut, and visually we can see the hole, but we can't just say "if it looks like a hole, it's a hole" because that causes the straw predicament. Imagine a point inside the center of the donut. Now, there is a 2d plane where the point is inside a circle, and it can't escape without using the third dimension. Now, imagine the plane moves perpendicular, so that it moves along the third dimension. We keep track of where it's moved by having the line leave a trail. Once the dot isn't contained inside the circle, we move on the other direction until we reach that same state. Now, the length of that line is how big the hole is, but what we care about is the fact it's all one line, thus meaning there's one hole. Now, if we did this to a straw, we'd reach the same conclusion. We need to stop caring about how far apart two openings are, and figure out if they're connected, because openings and holes aren't fully connected. Thus, a straw has one hole, never two.

[@olafzijnbuis]

Great video! What type of software did you use to create it? I could do a few of the basic shapes in Povray, but the transformations are stunning!

[@RacoonAndres]

probably blender

[@wannabewyvern]

Blender, you can see the blender font in some of their videos

[@awkarbi4646]

blender probably

[@souvikmandal2637]

Awesome ❤. Keep it up. Btw how you made these amazing animation?

[@antoniojpan]

Spectacular. Incredible amount of work to create this video. It is really a piece of art. Can you share the explicit formula for the deformation of the mug into the torus? I want to recreate it in mathematica, maple,...

[@mathscapsule979]

You are a great teacher

[@clarenscourtois8927]

Made my day 🤓!

[@chill_orange8374]

This adds more depth to my existential crisis.

[@ManDancingMoji]

Okay that solution was so cool.

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very nice

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What an AMAZING channel holy phokin sheesh

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Wow. Amazing.

[@matrixtech6917]

A very interesting video

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We want more videos!!!

[@robertarceo6560]

thank you

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Fucking. Masterpiece. Seriously great work m8, keep up the good work, had a great fun watching it!

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Please do more

[@kate8276]

Great videos!!!!))))

[@sparshgongale1943]

5:44 that was some cinematic art

[@Glen_Mali]

This is seriously tripping me out. How did it go from 1 hole to 2 holes

[@hede638]

so good

[@BoyKhongklai]

My brain hurts. Man I wish you uploaded more 👌👌

[@GITAISH]

SO ITS TOPOLOGY!!!! Since childhood i have this faint memories about mug that turn into doughnut, if recalled what i feel, it was existential dread

[@thalrosen]

you're the greatest

[@gregxu5142]

What's the music at 5:10? It sounds so familiar

[@diezelleprozo6047]

shoutout kabayan! just saw your video in my recommended section

[@dark_gamer197]

Pls post more video about topology I like ut videos

[@dipteshsarkat4661]

I like your video very much

[@mhffseriouslythisistaken]

What's the song in the background around 5:20-5:35? Piano opera.

[@zone07]

@6:09 not sure how the shape crossed the bar without breaking through.

[@AchrafTheGeek]

amazing video, just one complaint, during the puzzle solution, the camera focus effect , the lowed music and the camera movement were very disctracting

[@mehmet2247]

Ok, when will you broadcast the next video?

[@pawarranger]

puzzel soln part gave me goosebumps

[@pritamroy3766]

hi andrew, I have confussion with 1) homeomorphism 2) homomorphism 3) diffeomorphism, my questions regarding are can 1)two manifold be homomorphic as well as homeomorphic 2) two manifold be homomorphic as well as diffeomorphic 3)two manifold be diffeomorphic as well as homeomorphic .

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Start uploading video man. We need you❤.

[@alfredhitchcock45]

Mind boggling

[@harshplayz31882]

Waiting for some next interesting video...

[@yashsoni3835]

At 5:59 the first part slides over the second part and creates a hole, which changes the topology.

[@buildingfucker320]

Which tool did you use to animate 2d shapes

[@user-lh5hl4sv8z]

How does this only have 2k views

[@myworld4818]

i had 3 seperate thoughts while watching this video that i didnt want to think too long on and forgot them and they were super super interesting and i probably could've gotten accepted into harvard if i didn't forget 😭😭😭😭😭😭😭😭😭

[@braziliangentleman5148]

wait, it's all donuts? officer: "always has been"

[@sagarpuri7838]

7:05 for more info

[@voinea12]

It really goes to show what Jake is capable of

[@vishva8kumara]

3:00 It would be easier if we draw longitudinal lines for the sphere to count edges and surfaces.