Intro to Topology - Turning a Mug Into a Doughnut

Ғылым және технология

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 ...
Patreon: / andrewscampfire
Visit brilliant.org/AndrewsCampfire/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.
#SoME2
This video is sponsored by Brilliant.

Пікірлер: 207

  • @SorryBones
    @SorryBones2 ай бұрын

    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

  • @zaidyounas1602
    @zaidyounas1602 Жыл бұрын

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

  • @drewscampfire

    @drewscampfire

    Жыл бұрын

    Thanks, will do!

  • @c7hu1hu

    @c7hu1hu

    Жыл бұрын

    @@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.

  • @partybrawl1764

    @partybrawl1764

    Жыл бұрын

    @@drewscampfire I am also like him

  • @ITX635

    @ITX635

    Жыл бұрын

    @@c7hu1hu he lied he quit youtube

  • @ShanBojack

    @ShanBojack

    Жыл бұрын

    ​@@ITX635 how can u say that

  • @flyzo1977
    @flyzo1977 Жыл бұрын

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

  • @kjrey9878
    @kjrey9878 Жыл бұрын

    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!

  • @hishwaar
    @hishwaar Жыл бұрын

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

  • @ShaunakDe
    @ShaunakDe Жыл бұрын

    These animations are amazing!

  • @irodionzaytsev

    @irodionzaytsev

    Жыл бұрын

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

  • @symbolspangaea
    @symbolspangaea Жыл бұрын

    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

  • @carsonmcnamer5321
    @carsonmcnamer5321 Жыл бұрын

    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

    @drewscampfire

    Жыл бұрын

    Appreciate it!

  • @IAMASTICKSTUPIDPERSON

    @IAMASTICKSTUPIDPERSON

    Жыл бұрын

    @@drewscampfire yea try to post more

  • @hampusbrokmann8249

    @hampusbrokmann8249

    11 ай бұрын

    ​@@IAMASTICKSTUPIDPERSONwell it Cant be that long before there is a new video now 😂😁👏

  • @hampusbrokmann8249

    @hampusbrokmann8249

    11 ай бұрын

    ​@@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 KZread, easy to understand and clear pic of what you are talking about. Sorry for the dyslexia hope you understand 😂😂😂👏🇩🇰😇

  • @Alexander-xo5ho
    @Alexander-xo5ho Жыл бұрын

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

  • @nrml76
    @nrml76 Жыл бұрын

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

  • @RevShifty
    @RevShifty11 ай бұрын

    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.

  • @epalios
    @epalios Жыл бұрын

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

  • @opamp7292
    @opamp7292 Жыл бұрын

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

  • @sumirunihon
    @sumirunihon Жыл бұрын

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

  • @midohatem57
    @midohatem57 Жыл бұрын

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

  • @malicksoumare370
    @malicksoumare370 Жыл бұрын

    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.

  • @RealZynexx
    @RealZynexx Жыл бұрын

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

  • @jordanblack2250
    @jordanblack225011 ай бұрын

    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 🙏🤘🙌

  • @xplodingmojo2087
    @xplodingmojo2087 Жыл бұрын

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

  • @clarenscourtois8927
    @clarenscourtois8927 Жыл бұрын

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

  • @nataliaserhiienko9333
    @nataliaserhiienko93337 ай бұрын

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

  • @afsa376
    @afsa376 Жыл бұрын

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

  • @kamranshafiq2597
    @kamranshafiq259711 ай бұрын

    Excellent way to explanation. Surely you deserved millions of view

  • @father47_
    @father47_10 ай бұрын

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

  • @Quanlemon
    @Quanlemon Жыл бұрын

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

  • @nativeantarctican3325
    @nativeantarctican3325 Жыл бұрын

    What software do you use to make your amazing videos?

  • @drewscampfire

    @drewscampfire

    Жыл бұрын

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

  • @rasmusvanwerkhoven1962
    @rasmusvanwerkhoven1962 Жыл бұрын

    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!

  • @huvarda
    @huvarda6 ай бұрын

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

  • @goldfink2612
    @goldfink2612 Жыл бұрын

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

  • @tedfritzart
    @tedfritzartАй бұрын

    Just discovered this channel. Really wish to see more!

  • @cherry1leii
    @cherry1leii10 ай бұрын

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

  • @antoniuskonovalov
    @antoniuskonovalov Жыл бұрын

    Thank you, downloaded the Brilliant app via your link, worth it.

  • @peterpelle8982
    @peterpelle8982 Жыл бұрын

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

  • @sagarpuri7838
    @sagarpuri7838 Жыл бұрын

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

  • @endlesslovingmovement
    @endlesslovingmovement Жыл бұрын

    This is so well done! Amazing!

  • @Life_42
    @Life_42 Жыл бұрын

    Beautiful video!

  • @aditi28oct
    @aditi28oct Жыл бұрын

    We need more, keep up the good work

  • @souvikmandal2637
    @souvikmandal26376 ай бұрын

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

  • @BIackhole
    @BIackhole3 ай бұрын

    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!

  • @Swoger
    @Swoger Жыл бұрын

    another really good video from you!

  • @antoniojpan
    @antoniojpan10 ай бұрын

    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,...

  • @Qlust
    @Qlust Жыл бұрын

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

  • @olafzijnbuis
    @olafzijnbuis Жыл бұрын

    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

    @RacoonAndres

    Жыл бұрын

    probably blender

  • @wannabewyvern

    @wannabewyvern

    Жыл бұрын

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

  • @awkarbi4646

    @awkarbi4646

    Жыл бұрын

    blender probably

  • @Dhruva_P_Gowda
    @Dhruva_P_Gowda Жыл бұрын

    Nice Visualizations!!!

  • @WaleedHassanAwan
    @WaleedHassanAwan Жыл бұрын

    This video was so good ☺️ I loved it so much

  • @ivusofficial
    @ivusofficial5 ай бұрын

    Most mindblowing video I've ever seen

  • @geokou7645
    @geokou7645 Жыл бұрын

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

  • @jschmid26
    @jschmid2611 ай бұрын

    These animations are amazing, damn

  • @hossainahmmed6434
    @hossainahmmed6434 Жыл бұрын

    Keep them coming man

  • @maydimutawa8874
    @maydimutawa887411 ай бұрын

    That is absolutely awesome 👌🏻 👏

  • @srijani332
    @srijani332 Жыл бұрын

    Very very helpful... thanks...

  • @HAG47
    @HAG47 Жыл бұрын

    Amazing reall, keep up the good work

  • @xfa_f
    @xfa_f Жыл бұрын

    Love your vid man keep it up

  • @RSLT
    @RSLT Жыл бұрын

    Interesting. Great video!

  • @vasil_astrov
    @vasil_astrov Жыл бұрын

    Great video! Thanks! :)

  • @bumblebee9426
    @bumblebee94263 ай бұрын

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

  • @Leo-if5tn
    @Leo-if5tn Жыл бұрын

    Awesome video

  • @AchrafTheGeek
    @AchrafTheGeek Жыл бұрын

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

  • @igxniisan6996
    @igxniisan699611 ай бұрын

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

  • @mathscapsule979
    @mathscapsule979 Жыл бұрын

    You are a great teacher

  • @sparshgongale1943
    @sparshgongale19439 ай бұрын

    5:44 that was some cinematic art

  • @aithrasherboi
    @aithrasherboiАй бұрын

    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.

  • @bartekszachu7110
    @bartekszachu7110 Жыл бұрын

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

  • @SM-qw9tp
    @SM-qw9tp11 ай бұрын

    Interesting way to expand your mind.

  • @clarenscourtois8927
    @clarenscourtois8927 Жыл бұрын

    Made my day 🤓!

  • @kate8276
    @kate8276 Жыл бұрын

    Great videos!!!!))))

  • @ManDancingMoji
    @ManDancingMoji Жыл бұрын

    Okay that solution was so cool.

  • @cherylchui4510
    @cherylchui4510Ай бұрын

    Please do more

  • @y1729
    @y1729 Жыл бұрын

    Wow. Amazing.

  • @johnchessant3012
    @johnchessant3012 Жыл бұрын

    very nice

  • @robertarceo6560
    @robertarceo6560 Жыл бұрын

    thank you

  • @ayushjha3716
    @ayushjha3716 Жыл бұрын

    We want more videos!!!

  • @matrixtech6917
    @matrixtech6917 Жыл бұрын

    A very interesting video

  • @Glen_Mali
    @Glen_Mali Жыл бұрын

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

  • @d-e-p8473
    @d-e-p8473 Жыл бұрын

    What an AMAZING channel holy phokin sheesh

  • @gregxu5142
    @gregxu5142 Жыл бұрын

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

  • @chill_orange8374
    @chill_orange837417 күн бұрын

    This adds more depth to my existential crisis.

  • @dipteshsarkat4661
    @dipteshsarkat4661 Жыл бұрын

    I like your video very much

  • @hede638
    @hede638 Жыл бұрын

    so good

  • @mehmet2247
    @mehmet22477 ай бұрын

    Ok, when will you broadcast the next video?

  • @dark_gamer197
    @dark_gamer197 Жыл бұрын

    Pls post more video about topology I like ut videos

  • @adrenaline647
    @adrenaline647 Жыл бұрын

    i do love the hairy balls theorem Great video man, the way you explain things makes it much easier to understand 👍

  • @BoyKhongklai
    @BoyKhongklai2 ай бұрын

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

  • @mhffseriouslythisistaken
    @mhffseriouslythisistaken Жыл бұрын

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

  • @diezelleprozo6047
    @diezelleprozo6047 Жыл бұрын

    shoutout kabayan! just saw your video in my recommended section

  • @vishva8kumara
    @vishva8kumara Жыл бұрын

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

  • @GITAISH
    @GITAISH Жыл бұрын

    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

  • @TrigonometryX
    @TrigonometryX Жыл бұрын

    Just by 2 videos I’ve learned more than my entire career of school until my current grade (5th)

  • @alfredhitchcock45
    @alfredhitchcock453 ай бұрын

    Mind boggling

  • @AvinashKumar-vv4vd
    @AvinashKumar-vv4vd Жыл бұрын

    Start uploading video man. We need you❤.

  • @myworld4818
    @myworld4818 Жыл бұрын

    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 😭😭😭😭😭😭😭😭😭

  • @pritamroy3766
    @pritamroy376611 ай бұрын

    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 .

  • @thalrosen
    @thalrosen Жыл бұрын

    you're the greatest

  • @user-lh5hl4sv8z
    @user-lh5hl4sv8z Жыл бұрын

    How does this only have 2k views

  • @buildingfucker320
    @buildingfucker320 Жыл бұрын

    Which tool did you use to animate 2d shapes

  • @jameerlawrencebondoc8162
    @jameerlawrencebondoc8162 Жыл бұрын

    5:15 the color of the "handcuff" seems intimidating

  • @pawarranger
    @pawarranger Жыл бұрын

    puzzel soln part gave me goosebumps

  • @harshplayz31882
    @harshplayz31882 Жыл бұрын

    Waiting for some next interesting video...

  • @yashsoni3835
    @yashsoni38355 ай бұрын

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

  • @papope_i
    @papope_i11 ай бұрын

    acabo de encontrar este canal y me duele ver que haya dejado la actividad

Келесі