Intro to Topology - Turning a Mug Into a Doughnut

  Рет қаралды 79,539

drew's campfire

drew's campfire

Күн бұрын

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
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This video is sponsored by Brilliant.

Пікірлер: 208
@SorryBones
@SorryBones 2 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
@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
@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
@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!
@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
@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!
@Alexander-xo5ho
@Alexander-xo5ho Жыл бұрын
hands down the most interesting video about coffee mugs and donuts ive watched
@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.
@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.
@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 KZfaq, easy to understand and clear pic of what you are talking about. Sorry for the dyslexia hope you understand 😂😂😂👏🇩🇰😇
@sumirunihon
@sumirunihon Жыл бұрын
congratulations on your first sponsor deal, glad your channel is growing and keep it up!
@RevShifty
@RevShifty 11 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 😊
@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.
@midohatem57
@midohatem57 Жыл бұрын
High quality work, really liked your klein bottle video, highly underrated, keep going 👍👍
@cherry1leii
@cherry1leii 10 ай бұрын
Damn, Topology is something very different and I kinda begin to love it
@RealZynexx
@RealZynexx Жыл бұрын
So many good KZfaq channels like this popping up in my recommended section! Keep it up man, your videos are great!
@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
@jordanblack2250
@jordanblack2250 11 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 🙏🤘🙌
@antoniuskonovalov
@antoniuskonovalov Жыл бұрын
Thank you, downloaded the Brilliant app via your link, worth it.
@clarenscourtois8927
@clarenscourtois8927 Жыл бұрын
That was super great, I can understand 3d and some other things related to complex geometry better now. Thank you!
@father47_
@father47_ 10 ай бұрын
please continue making videos like this, they are super interesting!
@Life_42
@Life_42 Жыл бұрын
Beautiful video!
@huvarda
@huvarda 6 ай бұрын
This video is great! Definitely deserves more views than just 50k
@Quanlemon
@Quanlemon Жыл бұрын
Yoo only 4 videos and feels like you are a professional youtuber, you are a great inspiration❤️
@goldfink2612
@goldfink2612 Жыл бұрын
omg you have posted again!! i love your channel!
@Swoger
@Swoger Жыл бұрын
another really good video from you!
@tedfritzart
@tedfritzart Ай бұрын
Just discovered this channel. Really wish to see more!
@kamranshafiq2597
@kamranshafiq2597 11 ай бұрын
Excellent way to explanation. Surely you deserved millions of view
@endlesslovingmovement
@endlesslovingmovement Жыл бұрын
This is so well done! Amazing!
@aditi28oct
@aditi28oct Жыл бұрын
We need more, keep up the good work
@nataliaserhiienko9333
@nataliaserhiienko9333 7 ай бұрын
It's a pity that there aren't any new videos on this wonderful KZfaq channel😔
@ivusofficial
@ivusofficial 5 ай бұрын
Most mindblowing video I've ever seen
@peterpelle8982
@peterpelle8982 Жыл бұрын
watching ur animations bring me calm in this hard times of my metal health. THXS
@WaleedHassanAwan
@WaleedHassanAwan Жыл бұрын
This video was so good ☺️ I loved it so much
@jschmid26
@jschmid26 11 ай бұрын
These animations are amazing, damn
@hossainahmmed6434
@hossainahmmed6434 Жыл бұрын
Keep them coming man
@bumblebee9426
@bumblebee9426 3 ай бұрын
This is one of the best videos i’ve ever watched on youtebe
@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)
@Qlust
@Qlust Жыл бұрын
HI, I just wanna say your vidoes are really great and easy to understand!
@RSLT
@RSLT Жыл бұрын
Interesting. Great video!
@xfa_f
@xfa_f Жыл бұрын
Love your vid man keep it up
@geokou7645
@geokou7645 Жыл бұрын
A sponsorship of a large website with only 4 videos?!?!? This man is insanely good
@srijani332
@srijani332 Жыл бұрын
Very very helpful... thanks...
@Dhruva_P_Gowda
@Dhruva_P_Gowda Жыл бұрын
Nice Visualizations!!!
@HAG47
@HAG47 Жыл бұрын
Amazing reall, keep up the good work
@BIackhole
@BIackhole 3 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!
@maydimutawa8874
@maydimutawa8874 11 ай бұрын
That is absolutely awesome 👌🏻 👏
@igxniisan6996
@igxniisan6996 11 ай бұрын
If u keep going down in this rabbit hole of topology you'll finally come across with those sphere inside out guys
@sagarpuri7838
@sagarpuri7838 Жыл бұрын
This is next level explanations. amazing videos , keep it up. please make videos on fluid mechanics and semiconductor.
@vasil_astrov
@vasil_astrov Жыл бұрын
Great video! Thanks! :)
@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!
@souvikmandal2637
@souvikmandal2637 6 ай бұрын
Awesome ❤. Keep it up. Btw how you made these amazing animation?
@Leo-if5tn
@Leo-if5tn Жыл бұрын
Awesome video
@antoniojpan
@antoniojpan 10 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,...
@mathscapsule979
@mathscapsule979 Жыл бұрын
You are a great teacher
@ManDancingMoji
@ManDancingMoji Жыл бұрын
Okay that solution was so cool.
@SM-qw9tp
@SM-qw9tp 11 ай бұрын
Interesting way to expand your mind.
@johnchessant3012
@johnchessant3012 Жыл бұрын
very nice
@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
@clarenscourtois8927
@clarenscourtois8927 Жыл бұрын
Made my day 🤓!
@d-e-p8473
@d-e-p8473 Жыл бұрын
What an AMAZING channel holy phokin sheesh
@matrixtech6917
@matrixtech6917 Жыл бұрын
A very interesting video
@kate8276
@kate8276 Жыл бұрын
Great videos!!!!))))
@bartekszachu7110
@bartekszachu7110 Жыл бұрын
Fucking. Masterpiece. Seriously great work m8, keep up the good work, had a great fun watching it!
@y1729
@y1729 Жыл бұрын
Wow. Amazing.
@Glen_Mali
@Glen_Mali Жыл бұрын
This is seriously tripping me out. How did it go from 1 hole to 2 holes
@chill_orange8374
@chill_orange8374 20 күн бұрын
This adds more depth to my existential crisis.
@BoyKhongklai
@BoyKhongklai 2 ай бұрын
My brain hurts. Man I wish you uploaded more 👌👌
@diezelleprozo6047
@diezelleprozo6047 Жыл бұрын
shoutout kabayan! just saw your video in my recommended section
@aithrasherboi
@aithrasherboi 2 ай 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.
@ayushjha3716
@ayushjha3716 Жыл бұрын
We want more videos!!!
@robertarceo6560
@robertarceo6560 Жыл бұрын
thank you
@dipteshsarkat4661
@dipteshsarkat4661 Жыл бұрын
I like your video very much
@sparshgongale1943
@sparshgongale1943 9 ай бұрын
5:44 that was some cinematic art
@cherylchui4510
@cherylchui4510 Ай бұрын
Please do more
@hede638
@hede638 Жыл бұрын
so good
@dark_gamer197
@dark_gamer197 Жыл бұрын
Pls post more video about topology I like ut videos
@thalrosen
@thalrosen Жыл бұрын
you're the greatest
@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
@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
@user-lh5hl4sv8z
@user-lh5hl4sv8z Жыл бұрын
How does this only have 2k views
@gregxu5142
@gregxu5142 Жыл бұрын
What's the music at 5:10? It sounds so familiar
@mehmet2247
@mehmet2247 7 ай бұрын
Ok, when will you broadcast the next video?
@pawarranger
@pawarranger Жыл бұрын
puzzel soln part gave me goosebumps
@harshplayz31882
@harshplayz31882 Жыл бұрын
Waiting for some next interesting video...
@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 😭😭😭😭😭😭😭😭😭
@AvinashKumar-vv4vd
@AvinashKumar-vv4vd Жыл бұрын
Start uploading video man. We need you❤.
@alfredhitchcock45
@alfredhitchcock45 3 ай бұрын
Mind boggling
@TrigonometryX
@TrigonometryX Жыл бұрын
Just by 2 videos I’ve learned more than my entire career of school until my current grade (5th)
@voinea12
@voinea12 2 ай бұрын
It really goes to show what Jake is capable of
@vishva8kumara
@vishva8kumara Жыл бұрын
3:00 It would be easier if we draw longitudinal lines for the sphere to count edges and surfaces.
@yashsoni3835
@yashsoni3835 5 ай бұрын
At 5:59 the first part slides over the second part and creates a hole, which changes the topology.
@mhffseriouslythisistaken
@mhffseriouslythisistaken Жыл бұрын
What's the song in the background around 5:20-5:35? Piano opera.
@buildingfucker320
@buildingfucker320 Жыл бұрын
Which tool did you use to animate 2d shapes
@braziliangentleman5148
@braziliangentleman5148 Жыл бұрын
wait, it's all donuts? officer: "always has been"
@zone07
@zone07 Жыл бұрын
@6:09 not sure how the shape crossed the bar without breaking through.
@papope_i
@papope_i 11 ай бұрын
acabo de encontrar este canal y me duele ver que haya dejado la actividad
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