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 ...
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Пікірлер: 207
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
Hi andrew, i recently bumped into your channel and i must say i wasn't disappointed. Keep em. coming
@drewscampfire
Жыл бұрын
Thanks, will do!
@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
Жыл бұрын
@@drewscampfire I am also like him
@ITX635
Жыл бұрын
@@c7hu1hu he lied he quit youtube
@ShanBojack
Жыл бұрын
@@ITX635 how can u say that
5:42 wow that gave me chills very intersting continue with your videos they deserves so much more views I wish you success
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!
That handcuff puzzle was pretty cool. The 3D animation really helped with understanding. Great video!
These animations are amazing!
@irodionzaytsev
Жыл бұрын
Mindblowing! Even if you figure out the answer, it is still so incredible to actually watch the deformation!
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
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
Жыл бұрын
Appreciate it!
@IAMASTICKSTUPIDPERSON
Жыл бұрын
@@drewscampfire yea try to post more
@hampusbrokmann8249
11 ай бұрын
@@IAMASTICKSTUPIDPERSONwell it Cant be that long before there is a new video now 😂😁👏
@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 😂😂😂👏🇩🇰😇
hands down the most interesting video about coffee mugs and donuts ive watched
More videos on topology for non mathematicians please. You did a great job of presenting concepts in a very understandable way.
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.
I love this channel! You discuss topics im most interested about! Keep posting pls!!
These videos are awesome!!! I’m so glad to have found them and looking forward seeing more. Thank you so much 😊
congratulations on your first sponsor deal, glad your channel is growing and keep it up!
High quality work, really liked your klein bottle video, highly underrated, keep going 👍👍
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.
So many good KZread channels like this popping up in my recommended section! Keep it up man, your videos are great!
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 🙏🤘🙌
This is exactly like that one video where those two people turn a sphere inside out. You’ve earned my subscription.
That was super great, I can understand 3d and some other things related to complex geometry better now. Thank you!
It's a pity that there aren't any new videos on this wonderful KZread channel😔
I love how I got this into recommendations and I hate how I didn't know about this channel until today
Excellent way to explanation. Surely you deserved millions of view
please continue making videos like this, they are super interesting!
Yoo only 4 videos and feels like you are a professional youtuber, you are a great inspiration❤️
What software do you use to make your amazing videos?
@drewscampfire
Жыл бұрын
I use Blender and Manim! (both are free and open-source)
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!
This video is great! Definitely deserves more views than just 50k
omg you have posted again!! i love your channel!
Just discovered this channel. Really wish to see more!
Damn, Topology is something very different and I kinda begin to love it
Thank you, downloaded the Brilliant app via your link, worth it.
watching ur animations bring me calm in this hard times of my metal health. THXS
This is next level explanations. amazing videos , keep it up. please make videos on fluid mechanics and semiconductor.
This is so well done! Amazing!
Beautiful video!
We need more, keep up the good work
Awesome ❤. Keep it up. Btw how you made these amazing animation?
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!
another really good video from you!
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,...
HI, I just wanna say your vidoes are really great and easy to understand!
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
Жыл бұрын
probably blender
@wannabewyvern
Жыл бұрын
Blender, you can see the blender font in some of their videos
@awkarbi4646
Жыл бұрын
blender probably
Nice Visualizations!!!
This video was so good ☺️ I loved it so much
Most mindblowing video I've ever seen
A sponsorship of a large website with only 4 videos?!?!? This man is insanely good
These animations are amazing, damn
Keep them coming man
That is absolutely awesome 👌🏻 👏
Very very helpful... thanks...
Amazing reall, keep up the good work
Love your vid man keep it up
Interesting. Great video!
Great video! Thanks! :)
This is one of the best videos i’ve ever watched on youtebe
Awesome video
amazing video, just one complaint, during the puzzle solution, the camera focus effect , the lowed music and the camera movement were very disctracting
If u keep going down in this rabbit hole of topology you'll finally come across with those sphere inside out guys
You are a great teacher
5:44 that was some cinematic art
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.
Fucking. Masterpiece. Seriously great work m8, keep up the good work, had a great fun watching it!
Interesting way to expand your mind.
Made my day 🤓!
Great videos!!!!))))
Okay that solution was so cool.
Please do more
Wow. Amazing.
very nice
thank you
We want more videos!!!
A very interesting video
This is seriously tripping me out. How did it go from 1 hole to 2 holes
What an AMAZING channel holy phokin sheesh
What's the music at 5:10? It sounds so familiar
This adds more depth to my existential crisis.
I like your video very much
so good
Ok, when will you broadcast the next video?
Pls post more video about topology I like ut videos
i do love the hairy balls theorem Great video man, the way you explain things makes it much easier to understand 👍
My brain hurts. Man I wish you uploaded more 👌👌
What's the song in the background around 5:20-5:35? Piano opera.
shoutout kabayan! just saw your video in my recommended section
3:00 It would be easier if we draw longitudinal lines for the sphere to count edges and surfaces.
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
Just by 2 videos I’ve learned more than my entire career of school until my current grade (5th)
Mind boggling
Start uploading video man. We need you❤.
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 😭😭😭😭😭😭😭😭😭
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 .
you're the greatest
How does this only have 2k views
Which tool did you use to animate 2d shapes
5:15 the color of the "handcuff" seems intimidating
puzzel soln part gave me goosebumps
Waiting for some next interesting video...
At 5:59 the first part slides over the second part and creates a hole, which changes the topology.
acabo de encontrar este canal y me duele ver que haya dejado la actividad