A donut is not a sphere | Things you can do on one surface but not the other
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- Get free access to over 2500 documentaries on CuriosityStream: curiositystrea... (use code "zachstar" at sign up)
Get the "Don't be a Jerk" shirt here!: stemerch.com/c...
Support the Channel: / zachstar
PayPal(one time donation): www.paypal.me/...
Join this channel to get access to perks:
/ @zachstar
►Follow me
Instagram: / zachstar
Twitter: / imzachstar
►Original video I'm responding to: • These changed how I th...
►James Grime 3 Utilities Problem Explanation: • The Utilities Problem ...
►3b1b 3 Utilities on Coffee Mug: • Why this puzzle is imp...
►Wind on Torus Vs Sphere Video: • The second most beauti...
Animations: Brainup Studios ( brainup.in/ )
Check out my Spanish channel here: / zach star en español
►My Setup:
Space Pictures: amzn.to/2CC4Kqj
Magnetic Floating Globe: amzn.to/2VgPdn0
Camera: amzn.to/2RivYu5
Mic: amzn.to/35bKiri
Tripod: amzn.to/2RgMTNL
Equilibrium Tube: amzn.to/2SowDrh
►Check out my Amazon Store: www.amazon.com...
If you want to get the "Don't be a Jerk" shirt I'm wearing in this video, check out the STEMerch store for that and more!: stemerch.com/
Hey can you do more videos on biomedical engineering and what major is best suited for it. I hear mechanical and electrical engineers usually take BME’s jobs because a BME major doesnt have enough expertise. Is this true? Should i major in BME to become one as a career?
If the video is uploaded 1 hour ago then how is this comment was written 7 hours ago?🤔
Please make a video on what is mechatronics and it’s future
@@reetajain6463 look st his mechanical engineering sub fields video he talks about it
I hope you make a video about physical engineering
Of course a donut is not a sphere. Everyone knows a donut is a mug
I was looking for this comment
I know, I drink my coffee out of a doughnut
and humans are a 7 holed donut.
@@IdaeChop I don't think 7. I would say topologically there's three holes, aka two nostrils and the mouth. Since they're connected down to the anus that doesn't count as a fourth hole, also I think the eyes and the urethra can be deformed into a plain so it wouldn't count as a hole. I may be wrong tho
@@andreasapei2859 ears?
A better name for this video is: “Proof that a donut is, in fact, not a sphere.”
"why holes cannot be eliminated in rubber sheet geometry"
Why is no one talking about the ‘HAIRY BALL THEOREM’.
They are.
you mean hairy coconut?
Is this a real thing?
5:29
@@freedomtalesans4481 yes, it's mentioned in the video and you can check out the wikipedia article about it, it's very interesting
What I love about math videos is that the title claims that a donut is not a sphere and everybody is like: "Impossible! I need to know why."
Zach playing with balls.
Perfection.
Promotion video for his upcoming onlyfans
Well, if they're his, he has all the right.
a real zex star
Living upto his name I see mm hmm
Hairy ball theorems as well
A donut is not a sphere:
When u do your engineering watching interstellar and dark series
I know this isn't supposed to be a career video, but I've always found your videos on engineering super helpful and was wondering if you could talk about going from engineering to patent law?
Can you make a 3-dimensional Asteroids game with a four-dimensional doughnut?
A 3d asteroid
To make a 3D Asteroids game you only need a 3-torus, but a /flat/ 3-torus requires 6D space. In general, a flat N-torus needs 2N dimensions of space in which to live. This is because an N-torus is the cartesian product of N circles, and each circle requires its own plane in which to live. In 3D, the 2-torus isn't flat and looks the way it does because the 2 circle can't each have their own plane and are forced to share. ^_^
The only thing missing in this video is you playing a hacked asteroids without the asteroids, and showing that you can't form a contractible loop
wish our Engineering curriculum had such cool topics😌😌😌
Yeah...indian engineering sucks
@@Manoj-jj1dk So does Bangladeshi bro
indian education in general is shit, go abroad like my cousin did.
plan on going abroad myself once i get into college.
@@Manoj-jj1dk go to IITs(top 5) or IISc. U will get all of these.
Topology and engineering are quite seperate things
Just realized, the torus gives so much more "room" topologically speaking than the sphere that you could even fit a 4th house connected to all 3 utilities with no issues!
Woah
This is what I need now, something I don't understand to distract myself
2:16, does that mean if the arrow travels from one corner of the sheet to the opposite corner (i.e. 45 degrees), it would appear identical to a sphere? (obviously just for that case)?
Yeah I think so
"She found a pebble with a hole in it, which she kept in her pocket. Eventually the pebble wore a hole in the pocket and fell out, leaving nothing behind, but the hole." Terry Pratchett
Be careful
Rectangle at 1:58 is also not a sphere
It is projective plane, which even can't be represented in 3D with no self-intersections
As far as I know, some flat-earthers explain travelling over the edge like this. So they accidentally state that the Earth is not a sphere but a projective plane)
7:15 (pause this right here) this is a mugpostor/cuppostor in among us.
Basically an impostor made out of cups/mugs
*(All you need to do now is give it legs and feet, plus filling in that hole.)*
at 7:03, you can do it on a sphere because the sphere still has wraparound properties, so just go down with the water then once you wrap around, to the building on the right, then go to the right with the electricity then wrap around and go up to the house on the left.
These two don’t intersect because right before they would intersect, they’ve already reached their destinations.
That being said, it’s unrealistic to have wires and plumbing all the way across earth, especially when we have a 3rd dimension to work with
What is the max number of houses-utilities pairs can be placed on thorus with no intersections?
5:25 "there has to be 2" In fact, as Littlewood pointed out, the two can be the same point. (A cyclone and an anticyclone with a common centre and a common tangent.)
I would like to see a demonstration of the K5 graph as in the Asteroids plain
There might be donut earthers now
Question (Though I am not sure if he will see it):
Assuming the universe is a 4D torus but we are 3D beings, is there any way we could detect the difference between the 4D torus and a 4D sphere?
A that a donut , jelly filed are my favorite.
"Hairy ball theorem"
I spit out my orange juice!
Omg you are right, I never realized this, but donuts are NOT spheres
Isn't there a second incontractible loop for the torus, i.e. one which encompasses the hole in the middle?
A Donut is not a sphere. It is a coffee mug.
Why is it impossible to connect utilities on a sphere? At 7:00, you define a solution with two lines wrapping around to the other side of the plane.
I'm having trouble picturing it; but it seems like you could apply this solution on the sphere, no?
Is it impossible because those two 'wraparound' lines will always intersect somewhere on the back of the sphere?
Now to make a torus really mess with your minds. (Let's see Zach Star explain this one) Here is a corrugated torus where any direction you move on it's surface is equal distant from any other. IE if you traveled on the surface of this torus, around & through the hole, you would cover the same distance if you went around the outer O diameter. It would make it like a true square Asteroids universe if you lived on the surface... See doc here: www.ncbi.nlm.nih.gov/pmc/articles/PMC3358891/pdf/pnas.1118478109.pdf
Of website here: www.pnas.org/content/109/19/7218
Ignore the math, the first top left photo should illustrate the concept.
i want that mug official
Cool vid! Now I'm trying (and failing) to visualize a "universe" or game map that can be drawn as a square but the sides are connected in such a way that entering a wall, you exit the opposite wall, at the opposite position relative to the midpoint of the wall, at the opposite direction/angle... I can't determine if the exact corner would be infinitely (un)approachable or if they would just rebound the traveler or probably some alternative I'm not currently comprehending lol.. I'm thinking in order for this to work the square representation of the map would have to actually be at least two sections of the same "surface" (I really dont know what to call it) overlapped.. this is hurting my brain lol..
EDIT: So I figured out a way to visualize it, kinda like two spheres connected by a single point at which all longitudinal lines intersect.. idk if I'm explaining this well but its extra-dimmensional if it's even "possible"
because a cup is a torus u can do the utilities game on a cup
great as always
What if i have a sphere and magicly a hole apeares in the centre but without a cave going there. Basicly its like if earth äs core magicly disapeared. Would it be a sphere or a donut?
Hairy ball theorem. Heh. Heh heh.
Dammit. Now I have a hankering for donuts.
I actually had this problem
Yes they can, a donut has a back side and you can go around the houses on the top side as well
You cannot - by experiment - find a loop that is not contactable. Non-existence can not be proved by experiments.
Fitting to show a timbit on Canadian Thanksgiving.
Well that last one isn't a dobut, it's a donut *hole*
Now I want donuts
"Unless it's this kind of donut" WRONG! That's a DONUT HOLE! which is NOT a donut!
Dude a donut is not sphere...
7/11 dude: ummm yeah
No you dont understand how much its NOT man.
Ok, ok, I get it, a donut is not a sphere, but is it a rinsing machine or a washing machine?
Donuts and spheres are defined by what you can do on their surfaces?
The Asteroids' universe is not a torus, or else the asteroids would also wrap around.
I came here from Blue: Store Wolf rpg editor game
Well nice t-shirt.
It's saying "don't be a jerk"
Actually it seems to me that a torus would have NO contractible loops, or am i missing something?
No, there are lots of contractible loops.
Consider the torus (the flat one is easier to visualize). Draw a circle on the surface of the torus and it's contractible. But draw a straight line, then it's not. Both are loops on a torus.
A donut hole has no hole… 🤯
8:05
So I’m recalling from a class that a graph is planar on a 2d surface iff it contains no subgraph homeomorphic to K3,3 (the utilities problem) or K5. Since both of these can be drawn on a torus does that mean any graph is planar on a torus? Or did I just remember this incorrectly?
Neil Patram You’re right, but only on surfaces with genus 0 (i.e no holes). The surface of a torus is genus 1.
Aphrontic Alchemist so then it’s possible on a sphere but not a torus?
Neil Patram A I should clarify that the theorem holds for surfaces with genus 0. With that, does the surface of a sphere have holes?
So, we live in Taurus?
Hairy ball theorem? What are you guys smoking? Quantum mechanics?
Bring on the Donut Earth Theory to elevate
Flat Earths' circular reasoning to a higher plane, punintended! :) Sadly, its grifter 'Leaders' couldn't even try because they're dumb enough to repeatedly disprove their own 'hypothesis' in just 2 dimensions, so adding one more would break their brain. Nevertheless, a Donut Earth would be a very interesting hypothetical subject to explore.
I’m an adult and I laughed at 5:30
5:30
What is the meaning of the logo on the shirt, please.?
Don't be a jerk. The third derivative of position with respect to time is called 'jerk'
That's a torus, not a donut.
But what about a doughnut????
*cough* homology groups *cough*
Edit: you actually touch on that beginning about 4:00. Impressive. Are you _sure_ you're an engineer?😁
The video is published 2 minutes before and views are 60 but video is of 9 minutes and we know that when a person watches half video then it gets one views..then how 60 views possible in 2 minutes🙄🙄??
Edit:And most interesting thing,the pinned comment is commented 5 hours before😁 XD
Published =/= uploaded
Hairy ball theorem seriously.
did he really not fing any alternative to that name
Donut holes are not donuts! Only holed donuts are donuts that is donuts with holes but not donut holes. Do not donut the donut hole without a hole to donut. 😛
but are humans donuts?
are cows spheres?
This is probably a very stupid question, but why is it that on a sphere such as the earth you can go east or west infinitely and while you will loop on yourself, you will still always be going east or west, but if you go north long enough you will eventually be going south
In all my existence I have learnt two thing now:
1) Mitochondria is the powerhouse of the cell
2) A donut is not a sphere
and the word Ghazali?
1) Indeed they is!
3) A donut is, however, a coffee mug.
On a sphere, the 4 color theorem holds; on a torus, 7 colors may be necessary to color certain maps.
That's why you sometimes need 7 colours to paint a donut
@@hyu9648 its a common problem i run into when painting my doughnuts. keep having to buy new paints
@@Konomi_io I know right, I baught red, yellow, green and blue but then it's not enough to paint my donut so I had to buy purple but then that's not enough so I got orange and cyan and it's finally enough.
@@ordinaryshiba So, if you dunk your donut into dark chocolate first and use that as one of the colors, could you skip on cyan then? Asking for homework....
Huh
"A donut is not a sphere". Yeah but eating it makes you one.
Nice
And if someone squeezes you really hard, your cream filling will come out.
@@svfantom7776Correction: cum out
Topologically, the human body is a very complicated manifold because of all the blood vessels.
@@svfantom7776 omg shit that had me laughing so hard hahahahahhaha
imagine you're walking on Antarctica
and suddenly you show up in the middle of the arctic ocean
Thats not how that works, if Antarctica is on the bottom of the square map, and therefore the top as well, the Arctic would be in the middle.
Time to study the hairy ball theorem
Infrastructure architects after watching this video: "The world is a mug"
No it isn't...a mug has a hole, the earth does not.
@@kingacrisius how do you know it hasn't got a hole, have you visited every place on earth?
@@kingacrisius ah yes, _humorn't._
@@expolarity7541 If you pretend the magma layers of the earth are just air, then it does have holes, but it has more than one hole. If you realize that the magma layers exist, then there are no holes.
It is worth mentioning that a tangent vector field on a sphere only has (at least) to have two zeroes, if you count them with their multiplicity. It is perfectly possible to have a vector field with only one, weird zero.
Clearly, donuts and donut holes are two different things.
*Uhhh yeah dude you can clearly see from a top down view that it's a circle, bro.*
All in all, always awesome work!
"Donut is not a sphere"
*Always has been* it's a *_thicc_* circle obviously..
4:50 now i know what flat earthers are doing
If they could find a loop that's not contractable, it would prove we aren't living on a sphere. It would also prove we aren't living on a flat earth either.
You know how long I wanted to find the solution? 4 years. My friend told me about this riddle 4 years ago and I never figured it out
4:17
counterpoint: most would probably drown first
What does that "Don't be a
d³x/dt³" mean ? 😔😐
See the pinned comment!
d³x/dt³ physically is called *Jerk*
Velocity is the change in your distance over time. Acceleration is change in your velocity over time. Change in your acceleration over time is called jerk, because it causes the jerking feeling you feel when your speeding up or stopping a a car. We say jerk is the "third derivative" of distance over time because its the change in the change in the change of distance. When the equation says d³x/dt³ it means the third derivative (d³) of distance (x) over time (t).
TIL some mathematician came up with something called the "Hairy Ball Theorem".
Can you recommend some books about interesting stuff like this please
Euler's Gem
@@zachstar Any others...I mean anything that'll help me understand more of what you cover in your videos
@@ldrago2019 Shape of space, hyperspace, symmetry by marcus du sautoy, the numbers behind numb3rs, the man who loved only numbers, how not to be wrong
I love your dimensional videos. your videos are very 3 dimensional
3:14 This argument is not topological, as topology does not make sense of angle measures and orthogonality ; and thus it is not an argument to prove a sphere not being a torus topologically; it is rather geometrically valid. Correct me if I missed something.
I can think of way to make it a topological argument: Since both the sphere and the torus are 2d manifolds and thus locally homeomorphic to a plane, you can define the property of two tangent paths on a point to be locally homeomorphic to two tangent circles in a plane. After you define that, you say that on a sphere, any two closed paths that intersect at exactly one point are tangent on that point, but on a torus, you could find two closed paths that intersect at exactly one point, yet they are not locally equivalent to two tangent circles but rather to two intersecting lines at that point. And you see, these properties that we rely on are topological i.e they are conserved by continuous deformation, unlike angles, thus they are intrinsic properties of the topological abstractions of the sphere and the torus.
Clarification: By "locally homeomorphic on a point", I mean: there is at least one neighbourhood of that point that when being intersected in both cases with the individual paths, it makes two homeomorphic figures. And therefore it will be true for every smaller neighbourhood, hence the adverb "locally".
I hope this makes sense.
Did you describe the real protective plane in the first half of the video? It's not exactly a sphere.
“A donut is not sphere, unless it’s this kind of donut then different story” 🤣🤣🤣 BTW: first time seeing this channel and already subbed!
'but mom, i learn a lot of interesting stuff when on the pc'
'so, what did you learn today?'
'...'
I love spheres, jelly-filled are my favorite!
What if your universe is like the asteroid game, but on a massive scale? Would there be any way to know?
8:36 That is a donut hole, not a donut.
I want to see k5 evenly spaced on a torus with as much symatry as posible.
so a donut is not a sphere, but a donut hole is a sphere
Please make a video on what is mechatronics and it’s future
My next question would be: Is there any finite set of points on the surface of a torus where each point can be connected to all the others without any intersections, or is there some number or configuration of points that makes it impossible?
Is there a contractable loop on a donut?
A torus planet would be rlly cool
He said hairy ball theorem.
I bought a Ford Torus to do Donuts
Oh come on I didn't know it's 3D in the thumbnail. It's impossible in 2D.