Simple rules of geometry meant that 5-fold symmetry was impossible as were crystals without a periodic structure. This turns out to be wrong. Thanks to LastPass for sponsoring a portion of this video. Click here to start using LastPass: ve42.co/LPs

Huge thanks to Prof. Paul Steinhardt for the interview on this topic. Check out his book ‘The Second Kind of Impossible’

If you'd like to learn more about Penrose tilings, go check out "Penrose Tiles to Trapdoor Ciphers" by Martin Gardener, which helped my research for this video.

Filmed by Gene Nagata (Potato Jet on TRvid)

Animations by Iván Tello and Jonny Hyman

Editing, Coloring, Music & Audio mastering by Jonny Hyman

Prague scenes filmed in 2012.

Special thanks to Raquel Nuno for helping with the tilings!

Additional Music from Epidemic Sound

29 Eyl 2020

Çalma listem

Daha sonra izle

Veritasium Yıl önce

Roger Penrose was just awarded the Nobel Prize for Physics! Not for this pattern but “for the discovery that black hole formation is a robust prediction of the general theory of relativity”

shourya 👍 3 gün önce

Hats off to you, am I the first person to realize that this videos ratio is the golden ratio?

enrique11 15 gün önce

Is the ratio of the width of the long line to that of the short line also the golden ratio?

Human person 25 gün önce

Hexagons are bestagons

Matthé Uijttewaal Aylar önce

you cannot get an irreversible solution from a time-independent theory...

Ali Chehab Aylar önce

One of the most interesting classes I ever had

Blight Yıl önce

I feel like i learnt alot while learning nothing at the same time

SpiritsOfWolves 7 gün önce

Im not understanding any of this 😵💫

That1weirdnoob 8 gün önce

Same as this polar guy

Oliver and harry 9 gün önce

Agreeable

KingK117 9 gün önce

yes

Lexie’s Gaming 9 gün önce

Yes

Elliott Bork 6 aylar önce

I love when math people describe stuff as “the most five-ish” which makes absolutely no sense but makes a ton of sense at the same time

Elliott Bork 2 aylar önce

@Jordan clever….

Jordan 2 aylar önce

I love when people describe stuff as "math people" which makes absolutely no sense but makes a ton of sense at the same time

Shaoyi Sheng 3 aylar önce

Something interesting that Derek touches on but doesn't go into too much detail here is why it is that there are only 3 ways to tile a plane with regular polygons (the square, triangle, and hexagon) and why there are only 5 regular polyhedra. The reason for both of these ideas are intimately intertwined, and are shockingly purely arithmetic consequence of a simple geometric formula. According to the Euler characteristic, for any polyhedron the number of vertexes minus the number of edges plus the number of faces is equal to 2. For example, a cube has 8 verticies, 12 edges, and 6 faces, and 8-12+6 is 2. Also, note that for any polyhedron each face must have 3 or more edges, and 3 or more edges have to meet at every vertex. This point is really obvious if you try to build a 3d shape with 2 edges to a face or 2 edges to a vertex-- it just doesn't work. Let's say you have a regular polyhedra with p edges per face, and q edges per vertice. In this case because every edge is shared by exactly 2 faces, and every edge is shared by exactly 2 vertices, pf=2e and qv=2e. If this is confusing, imagine a cube. A cube has 6 faces, and every face has 4 edges. But because every edge borders two faces, it has (6*4)/2=12 edges. The same math applies to the vertices. You can rearrange the above to get f=(2e)/p and v=(2e)/q. But because of Euler's characteristic of polyhedrons, v-e+f=2. Simple substitution yields (2e/q)-e+(2e/p)=2. If you divide the previous equation by 2e and rearrange, you get (1/p) + (1/q) = (1/2) + (1/e). Now, if each face has 6 edges or more, it means that p ≥ 6, which means that q ≤ 3. However, that means that each vertex would have 2 or less edges, which is impossible. Thus p

ninty 11 gün önce

joke about there being 48 regular polyhedra here or something

Kevin Wu 24 gün önce

@hatixhe lacka to tile a shape is to be able to fill an infinetly large surface without leaving any gaps using only said shape. The only three regular polygons that can tile are mentioned in OC's comment

hatixhe lacka 24 gün önce

Ur a bit too smart man can u speak English?

Kevin Wu 29 gün önce

@Gabe Darrett yes, because they suck and literally have no use. They can't even tile properly unlike octagons.

Gabe Darrett 3 aylar önce

Is this the reason why heptagons (regular 7-sided polygons) don't appear in nature?

ZMacZ Furreh 7 aylar önce

Also, the Penrose structures can yield interesting cryptographics results, since the distance can't be calculated (beyond certain distances) and yet have a fixed shape once a certain set is known. It can also be used for quasi random generation in procedural generation for gaming worlds. (The latter is my favourite)

ZMacZ Furreh 11 gün önce

@Lord Felidae Since there's only few ways the pattern can be made to fit, once the first pieces are known, the positioning can be made as a set of numbers where the first number indicates the first piece it connects to, the second indicates the side for which it connects, and the third then being the side of the connecting piece it connects to, and the fourth being the type, and so on and so forth. Then adding more and more pieces you get a number string. Picking a set of like the 20th number in a row for each piece gives quasi random, but repeatable results, especially when the 'seed' is the Nth piece to the ever expanding set. Each string of ten decimals from that point is a base 0

Lord Felidae 17 gün önce

Can you give any examples so I can see exactly what you mean?

Tarmo Lattu 7 aylar önce

Penrose tiling also appears in the middle of Helsinki in Finland. A large walking street is covered in the pattern spreading up to a hundred meters. It was selected over various "regular" patterns. Really cool!

AFK_BIN Yıl önce

One of the most interesting classes I ever had

Annoying 17 year old 2 aylar önce

@Jordan Yes lol

Jordan 2 aylar önce

@Annoying 17 year old do you change your youtube username every birthday?

Time is Fading 4 aylar önce

Yea

waya 4 aylar önce

yes

Hoa Ngo 8 aylar önce

Bruh

Bas de Jong 5 aylar önce

Also a fun trick to do when a few of these patterns are shown simultaneously is by squinting your eyes until the edges of the area are perfectly in line. You'll see that all the matching patterns show up as normal, but the parts where they're different you see almost flashing zig-zag lines.

Rastko Vuković 7 aylar önce

An interesting, very well done and inspiring video. In the background of periodic and non-periodic paving of an infinite surface with a small number of samples, an analogy can be seen not only with the rational in relation to irrational numbers, but also with the "world of outcomes" in relation to the "world of possibilities".

CZ 7 aylar önce

Im a textile print and pattern designer and professor who teaches symmetries and tessellations but im not a mathematician. I just learned something new, thanks a lot!

Retro Plus 7 aylar önce

I can't believe school tricked us into believing mathematics was boring

David Sallge Yıl önce

This reminds me of an old saying we have here: "Everyone said that it was impossible. Then someone came who didn't know that and just did it."

TotoIsAyal 3 aylar önce

@Derp Atel like that one thing were I have a chance to walk through a wall.

TotoIsAyal 3 aylar önce

@Get on the cross and don’t look back a guy in the video is just talking about a cool pattern tf does cool flying book of rings have to do with this

Derp Atel 4 aylar önce

impossible's a myth.

Camilla A 4 aylar önce

oh also the saying with bees "According to all known laws of aviation, there is no way a bee should be able to fly. It's wings are too small to get its fat little body off the ground. The bee, of course, flies anyway, because bees don't care what humans think is impossible."

Deletus 4 aylar önce

LMAO!

Patrick Modin 2 aylar önce

This is one of my favorite Veritasium videos so far!! Very intuitive, however can you demonstrate the vertices rule with the tiles?

Александра Лебедева 4 aylar önce

"what exists because we just can't percieve because it's considered impossible?" is such a beautiful and impactful question. how much have we dismissed because we couldn't believe it could exist? how much have we overlooked?

Ali Chehab Aylar önce

This man's enthusiasm, individuality, and presentation is quite the treat. These are the types of teachers kids need to stay focused and excited.

Not Fiction 7 aylar önce

Mind blown. Also, I now have an inexplicable urge to tile something in a Penrose pattern.

No Yıl önce

My mind was blown several times through the course of this video, well done.

Theo Mossop 5 aylar önce

There is a theory that Penrose tilings are actually just a 2D slice of of a periodic structure in 5 dimensions

Joji Joestar Yıl önce

@Vijaz555 I don't hop on youtube with the expectation that every video is going to "boost" my life. On the contrary, youtube is a big time waster. I would say this does fascinate me as I have heard of quasicrystals before but did not quite understand them. So yeah made my day a bit better.

Vijaz555 Yıl önce

does knowing this make your life any better though?

Max Loh Yıl önce

I've been watching this guy's videos; they used to be quite interesting but nowhere near the mind-blowing quality of this one. One thing I know for sure: This guy just keeps getting smarter and smarter, and that makes me happy.

calholli Yıl önce

lol.. I said the same thing.. Glad I'm not the only one.

Anthony Wade 3 aylar önce

Hats off for the editor, most mind-blowing animation I've ever seen

LawsFreeLanceMalice 3 aylar önce

I’m downloading this video so perhaps when I’m next time drunk I might pick up more. 😁 The graphic pictures of geometric shapes made seeing your descriptions so much more interesting/amazing and I kept feeling like I was experiencing eureka moments. Those two pieces of acetate revealing deeper patterns close and far blew my mind. Thank you for creating this complicated video/topic more accessible for all.

Matthys Loedolff 3 aylar önce

The Chemistry Department (School of Molecular Sciences in the Bayliss Building) at The University of Western Australia has the Penrose pattern as floor tiles of the foyer and ground floor. Quite impressive when viewed from the top floor.

💜kookie💜 6 aylar önce

I love the way he explains everything it's so interesting if it was a part of my textbook I wouldn't have find it that interesting

Shota Toriumi Yıl önce

Me: Gives this pattern to the guy tiling my kitchen Tile guy: Sweats profusely

Lilly Cahill 10 aylar önce

LOL

Draconicさん 10 aylar önce

@Zhong Ping that's why you use matching rules on the vertices and not just on the edges

BumbleBeagan Yıl önce

stolen comment bro

irvanm87 Yıl önce

🤣🤣🤣

Zhong Ping Yıl önce

When a mistake doesn't become apparent for another 4 hours of tiliing

ZMacZ Furreh 7 aylar önce

12:20 Actually you can tell them apart. Each tile only has a number f set ways they can attach to another. So, once you know those, you can simply take one tile, and see in which positon and which type is connected on which side. This then yields a finite number, between 1 and the number of possible connections, where another tile connected then yields another position out of a finite set of connections. When and where these numbers occur in an infinite non-repeating loop, you can then state how 'far' they are apart, and thus have a relative position between them. Ofc, the math to actually calulate this, is extremely complex, possibly yet to be invented, and the computational power required may also need inventions unknown to us at this time, and yet, it could be done, since it involves a finite distance between each of the relatives, and where there's finite possibilities it can be calculated.

ZMacZ Furreh 5 aylar önce

@Juulesmann Bean The tiles themselves are repeated. The forms that are generated from one to the next is finite.The pattern can stretch to infinity, that's true. But within each set of tiles, no matter how large save infinite, there's only so many permutatons. This then allows for differentiation throughout the patterns. In fact start with any of the given single tiles, you get maybe one solution for each side that's fitting, but if there's more than one, you give the tileset a number which then corresponds with teh numbering of each tile. 4 pieces, (1-4), for each such permutation, along whichever axis going clockwise. Now you have numbered it's complexity through a number sequence, differentiating between them for anything but an infinity tileset. With these numbers being sequenced you now have a list of possibilities, which is also finite. So yeah, you can make it infinitely large in theory, but practically you can only make a finite one, and thus differentiate. The first number will indiicate which of the 4 sequences is used when coupled to the first tile, while the rotation of the initial tile is set per definition of each tile's shape. Btw, this tileset can lead to fantastic cryptologcal solutions.

Juulesmann Bean 5 aylar önce

No, that just means that certain portions of the tiling will be the same but not repeatable, as in you can’t take a certain portion and just attach it to itself to get another valid portion

David Lefebvre 3 aylar önce

I really appreciate this video. It took many of the things thst I have known for a long time and really put a great picture on how everything went together. You remind me of my favorite teacher. God bless you.

Velin 4 aylar önce

This man's enthusiasm, individuality, and presentation is quite the treat. These are the types of teachers kids need to stay focused and excited.

Noot noot Ima boot Aylar önce

i used to play with those penrose tiles with the arcs! it's actually really satisfying to know now that the pattern Can't repeat as expected lol

Peter S. Fam Yıl önce

If a floor was tiled with this anti-pattern, I think it would drive me slowly to madness looking for a pattern

Forest Armstrong Yıl önce

Mathness

corey Yıl önce

@marine biologist man Oooop-

auranecho Yıl önce

@porterde08 did you ..... watch the video

Michael_Zaki Yıl önce

I feel like the lack of any pattern is satisfying in it's own way.

Umora Mayori 7 aylar önce

Well, constantly seeing repeating patterns in the "non repeating patterns" makes this video rather confusing. For a non repeating pattern you should not be able to pick up a segment of tiles and be able to place them anywhere else across the plane.

Theo Mossop 5 aylar önce

It's not that the patterns don't recur, it's that they don't recur consistently. If you take the distance between a section and where that section comes up again, you won't necessarily find the section if you go out by that distance. The part about the parallel lines explains it well, it goes LSLSLSSLSLSLLSLS or whatever, you can find infinitely many segments of LSL or SLS or even LLSSLL but the pattern is not periodic. Its like in the number pi - you can find any and all digits, or even phone numbers in it, and you can even find them infinitely many times, but does that mean the number is rational?

Daisy Belle 7 aylar önce

I must say, videos like this ALWAYS haunt me! I begin thinking so hard that it hurts my head; going based on THIS.. So does this mean no two pictures taken will ever be the same? Based on everything being impossible to replicate? Say an image of two people, doing the same thing in the same place? .. Does that make sense to anyone else?

Beybrain78 Aylar önce

As for the golden ratio thing, what if you just add another dart from that pile you have behind you? Then it's not the golden ratio anymore. You just coincidentally took a certain amount from the box to get that ratio. If the pattern was truly infinite then the pattern wouldn't have this ratio to begin with since there's infinitely too many pieces to count.

Ali Chehab Aylar önce

I love when math people describe stuff as “the most five-ish” which makes absolutely no sense but makes a ton of sense at the same time

Anjiru Hyure Yıl önce

Isn't it weird how this could be a lecture in some school and we'd all be falling asleep, but this guy managed to make it so interesting that 3m people decided to watch it?

K ne 4 aylar önce

Oh nvm you meant 3 million i was watching this at 2 am

K ne 4 aylar önce

3am people?

Pushkar Anand 6 aylar önce

Now it's 14 m

mike jones 7 aylar önce

14 million now

Leyren Yıl önce

As a teacher, you don't have the time to put in as much effort into a few minutes of content than a video does. Producing something like this takes weeks. Including scripting, filming, visualizing and editing.

Felix Nielsen 8 aylar önce

I absolutely love this video, and have been watching it multiple time, since it was release, but one question has been nagging me. Shouldn't it be possible to do with one type of tile? Well, it is (using the rhombic Penrose tiling), if you look to the third dimension, and use golden rhombi, as is also evident when looking at the projection of the Rhombic triacontahedron (one of my absolute favorites) I have been doing some practical testing, and it seems to work out, but of course I cannot test in the infinite plane, and thus cannot say if the same rules and/or restrictions apply. I would very much like to know. ;)

Potato Tornado 3 aylar önce

If I recall correctly, this is an open problem called the Einstein problem.

JHaz 4 aylar önce

No, Felix the cat

Servant 2 aylar önce

Wow... incredible finds. Makes me think of our Creator with each discovery. Also, this video is very well done and you appear to be incredibly smart. Well done.

Lillith Nemesis Freyja Hecate 7 aylar önce

I saw this exact pattern during a DMT trip, never thought I'd see it again!

Charlie C 24 gün önce

The tiles reminded me of this incredible game I picked up on a trip to Germany in a traditional fairy tale toy store a few years ago! "Walong" is the game and the tiles are all the same curved irregular shape with hooked curls all over. I wish I had ten or thirty boxes of pieces to see how far the presumed infinite pattern can go. Would @Veritasium be able to apply any of the mathematical testing on the other tiles/patterns in a further examination.

Bridge_Frog Yıl önce

Honestly, this is quite entertaining. I didn’t expect patterns to spark my interest today-

just another account 5 aylar önce

Idk, my curiosity in patterns sparks up every now and then, usually at regular intervals. So judging by my previous behaviors, this was to be expected

april 5 aylar önce

@Your funni Boi hhhj

j 10 aylar önce

yeah and now im scared of the golden ratio

The_silvermario Yıl önce

I agree

Milo Verreijt 8 aylar önce

Amazing video! I learned alot this was really enjoyable.

Laura Bomhoff 4 aylar önce

These patterns are so pretty with such deep meaning. I would like to see them printed on clothing. Also tile work in homes. As art.

Dimitri Isov 3 aylar önce

When he revealed the golden ratio is at the center of all this I felt myself align with the cosmos.

SaucePan Aylar önce

I wonder if this conjecture was plugged into a quantum computer, would it truly yield an infinite conclusion? Or perhaps a incredibly massive number that we only now perceive as infinite?

Lil Bank account Yıl önce

Imagine finding over 20,000 tiles so that you could prove your professor wrong

Petaurista Yıl önce

@Lil Bank account It's not about triangles?

felixthehuman Yıl önce

And then imagine having Linus "the cure is megadoses of Vitamin C" Pauling call you a quasiscientist.

Lil Bank account Yıl önce

@Petaurista Pythagorean theorem

Petaurista Yıl önce

Actually it's simply from definition of infinity. Any finite number of combinations repeats in infinity. And in theory: also infinite numbers.

Surf Ninja 5 aylar önce

Does anybody know what Penrose patterns Derek use when he demonstrates the alignment with the transparency over the other pattern?

WaffleFriedRice 7 aylar önce

I want an entire series of anything and everything that was discovered solely due to curiosity of the complexity of a snowflake.

Frog-Boi7 4 aylar önce

I love how a video about tiles turned into essentially multiverse theory

Ardy Visser 2 aylar önce

the golden ratio always hits you when you least expect it

Aspen Eatherton Yıl önce

“Well it’s infinite, so it’s gotta repeat at SOME point, right?” Scientists: “lmao no”

Osi playz RBLX 4 aylar önce

Scientists: Nah we make the rules here LMAO

Itismethatguy 8 aylar önce

@Miniclash wait but then phi repeats?

totallyrad 10 aylar önce

so basically There are little patterns that repeat but there can never be the same large pattern? I'm still confused. my limited amount of brain cells are dying.

TheDevilsAngelGaming Yıl önce

how do we know pi is infinite how do we know it doesn't ever repeat if it's truly infinite then it has to repeat at some point we cant prove it's infinite until we see the end, which is impossible if it's infinite

Scott Miller 8 aylar önce

This is the why I enjoy Star Trek and similar types of science fiction, ones that take the science relatively seriously but assume that someday we'll find a way beyond the barriers we perceive. Because all it takes is one person with an idea, and then a second person taking it in a different direction. And suddenly, the future is something no one had ever thought of.

Kyle Moore 4 aylar önce

Man, it really feels impossible to tile a plane and never have the pattern repeat anywhere? Mind boggling. It feels like it’s kind of beyond our perception to an extent to imagine something infinite (hard enough as it is) only made of two shapes and you can never find a square of them that repeats despite the same shapes going on infinitely.

Ali Chehab Aylar önce

One of the most interesting classes I ever had

George Flitzer 3 aylar önce

This was utterly fascinating to me. Great video!

Shaun carter 11 aylar önce

This whole Golden Ratio is fascinating. It keeps popping up all over the place. I dig it.

Aqeel Aadam 17 gün önce

@Ezekiel Johnson I dunno

Ezekiel Johnson 17 gün önce

@Aqeel Aadam What's death?

Aqeel Aadam 17 gün önce

@Ezekiel Johnson I heard he died of ligme

Arthur wayne 2 aylar önce

@LeaveBritneyAloneOkay....I totally respect what you believe because it's your choice and I can do nothing about it. But just think about it, Why you have 10 fingers,why not 5,why not 7? Why trees are made with wood and leaves why not with iron and meat? We plant seeds but the tree that comes out from soil and it's structure are not in our hand. We do sex but the baby and it's structure that comes out of mother is not in our hand. We just do....but we didn't design ourselves neither trees or everything around us. How beautifully designed this nature is! How beautiful trees are, how gorgeous we human are! how marvelously beautiful our design is! Which has not a single mistake! Who made all of this? Yet we think no one designed all of these...It all came from no where.

LeaveBritneyAlone 2 aylar önce

@Arthur wayne you do you it's all good , I know Muslims who are happy being Muslim I know muslims who converted christian and Christians who converted Muslim it's all good everyone has the right to believe exactly what they want to. Religion in general is not the way i lean.

Mickatju_ 110 Aylar önce

Well then i have another question: can you do all this in 3D or is that impossible?

cryzz0n 3 aylar önce

The series of events that led to me watching this video are kind of insane. It all started with a picture of a pyramid of eggs on Facebook asking how many eggs were in the pyramid, that led me to looking at the sequence 1,5,14,30 etc. Numbers known as square pyramidal numbers, that led me to looking at sphere packing, which led me to Johannes Kepler, which then led me to tiling the plane, which lead me to Penrose tiling, which then led me to quasicrystals, and that led me to this video. All because of a picture of eggs on Facebook.

ZMacZ Furreh 7 aylar önce

The Kepler conjecture also returns in high pressure environments where atoms are forced into positions otherwise impossible due to the atomic structures normally at rest, or near rest. You can see this when examining ice, which has over 12 states, of which regular ice and water and water vapor are but 3. Once the presure goes up (like >220MPa) the other forms of ice molecule stacking become apparent, and they do so under atomic angles within the ice molecule that otherwise not apparent, like Ice-IX, also, when the temperature becomes really low, without additional pressure a natural rest form of Ice, Ice-XI also becomes apparent. But in all, when enough force is applied by pressure, other types of 'stacking' appear, and these then also must take up less space. For no change happens, without a different 'stacking', and since this is due to pressure, it must somehow mean that the 'stacking' involved is also more efficient.' Please note that the 'stacking' differently is possible since the form of the ice molecule is not symmetric beyond one line. And that the amount of pressure determines the way it actually gets stacked, while the shape of the iice molecule gives in to the pressure to be stacked that way.

Devon Bradbury 2 aylar önce

One of your lessons that undeniably cracked a paradigm or two in this head! 🤔

Hannah R Yıl önce

I’d like to point out this dude hated his professor so much, he looked at 20,000 squares just to prove him wrong

OtherAccountGotHacked 9 aylar önce

Spite fuels invention just as much as necessity

Lea Yıl önce

@radioactivedarkness r/wooosh

Shiromi Torayoshi Yıl önce

I feel so bad for the person who originally wrote this comment, Hannah R. All she wanted to do was to write a funny comment but ended up with a bunch of idiots in the reply section arguing over what a joke is. Jeez, don't you guys have anything better to do???

Manny Khosbin Yıl önce

Me: Gives this pattern to the guy tiling my kitchen Tile guy: Sweats profusely

Dr.Mikizzle Therapist Yıl önce

I’d like to point out this dude hated his professor so much, he looked at 20,000 squares just to prove him wrong

PoTato Head PokéMario 2 aylar önce

If each part of the pattern appears an infinite number of times on any pattern how is it impossible to force it to repeat?

Bilal Rida Aylar önce

Question: so if you begin in the same way for aperiodic tiles do you end up with the same pattern?

CJ Carpenter 7 aylar önce

The bit with the long and short gaps between parallel lines reminds me of genetic coding.

ALEX BERMAN 4 aylar önce

i am so happy to see millions of views for this kind of videos - it gives me hope that not all people are complete idiots in this world. Best channel ever!

Brianna Warren Yıl önce

Imagine having Penrose tiling in your bathroom floor. It's a very cool pattern, it'd be great to look at while you're otherwise occupied.

Shafa NT. 8 aylar önce

My house only has square tiles with simple patterns on them, yet I always find them interesting because the randomly rotated ones made a new shape that doesn't exist in the pattern. Man..I really need to stop looking at them ;-;

Fareed Abi Farraj Yıl önce

Yeah just it'll cost a bit too much🙈

Twisted Code Yıl önce

Funny enough, finding the part of the shape on a bathroom floor that makes the pattern periodic is something I often do while "otherwise occupied". If I ever come across a Penrose tiling now, I'll (hopefully) know better than to sit forever because you said that ;-)

ExHydraboy Yıl önce

@Richard Pike crusty mmm

miniwheatz93 Yıl önce

My thought exactly! Just need to determine how to not mess it up

Arun Maiti 3 aylar önce

Oh veritasium, your child like playing with the patterns makes the video an epic. Please make more of these kind of videos on other mathematical topics like geometry, topology. I have learned a lot from this video even after becoming a scientist working in this field.

Ozone Aylar önce

I really enjoy all your videos, as well as this one! But in contrast to all the other scientists you credit, these "tiling the plane" guys, had just too much time on their hands!

Vincent Tavani Aylar önce

Penrose is such a perfect name for someone who discovered a nearly five-fold symmetrical tiling.

HHK 7 aylar önce

The tilings, exhaustively explained, both periodic and aperiodic, are 2D; right? But then there is a sudden jump to 3D, with quasicrystals. Can there be an exhaustive well explained sequel on 3D tilings, that is, on 3D periodic and aperiodic patterns, or on the relationship between 2D and 3D patterns. Thank you..

Aquanimius 11 aylar önce

This man's enthusiasm, individuality, and presentation is quite the treat. These are the types of teachers kids need to stay focused and excited.

Robertas Kazlauskas 3 aylar önce

@Dain Fuentes You are right. Teachers are there to teach students. However, if their delivery is boring, students are going to get bored and will stop listening. As a teacher you are responsible to do your best to keep the attention of students so that they learn as much as they can from your class, be it by using humour or interacting with the class more. As soon as you lose their attention, they arent learning from you and their minds drift off to something that will actually stimulate their minds. For example, my physics teacher does a great job of making each class enjoyable, whereas my chemistry teacher drones on and on each class. I absolutely despise going to chemistry because her classes make me sleepy when i might have work the same day right after school. Whenever i can i just dont show up to her classes because i know im not gonna learn anything, whereas i actually want to show up to physics cause my teacher makes it not only bearable, but actually enjoyable. So no, the students are not responsible, it is the teachers responsibility.

Trubiso 3 aylar önce

@Dain Fuentes but they aren't there to give long boring classes where they just speak on and on without even checking on who they're talking to, I find it much better if the teacher makes the class engaging so I can actually focus on it because otherwise I'll find a distraction and the class will have been useless

Dain Fuentes 3 aylar önce

@Darren Gedye I'd say a lot of the responsibility lies with students who place priority on the nonverbal aspects of communication rather than the information being conveyed. The extent to which a teacher is perceived as being passionate has no bearing on whether the information being taught is correct, useful, etc. Teachers aren't there to be entertainers.

The Great British Circus Featuring Bojo 4 aylar önce

my year 7 science teacher was amazing,childish but not immature of that makes sense.he made science fun for the whole class and was just genuinely a good teacher

PianoGesang 5 aylar önce

The man is a genius

LiveXFreak 6 aylar önce

I've never finished school but watch alot of these videos, my little cousin taken physics loves talking with me because I know alot of what he's talking about, mostly from this channel, vsauce and Manny more :) just wanted to share

Creative Jay 8 aylar önce

What happens when we can use 4D? I have a feeling once technology gets to that point, Which may make anyone throw up wearing such a headset to see 4D, physics will change completely.

KJ64Gaming 8 aylar önce

I'm absolutely mind blown by the math involved in this!

Desmond's Corner 7 aylar önce

"what exists that we just can't perceive because we've convinced ourselves it's impossible" is super powerful, and i love it, but i also love its companions "what do we perceive that experts scoff at because everything they know says it should be impossible" Example: the anthropomorphizing of animal behavior [or "birds, bugs, and reptiles can't have emotions stop calling that raven saving a hedgehog's life cute"] "what can exist that we deny because it challenges our entire view of the world and of ourselves" Example: Artificial Intelligence cannot exist/Artificial Intelligence cannot have emotions

Hugo Bethancourt Yıl önce

As a physics and mathematics major I can’t find any video of Derek’s that isn’t totally enthralling. Let’s all take a moment to congratulate Penrose for his prize and Derek for such consistency and quality in all of his videos. You truly make the world a better place!

Prakhar Gautam Yıl önce

“As a physics and mathematics major”

Tobias Rogers Yıl önce

@Beau Saunders lol

monir kinder Yıl önce

@Beau Saunders why so?

Beau Saunders Yıl önce

I haven’t enjoyed a video of his for years

muggy ate 3 aylar önce

now I wanna see this as a part of an algorythm to procedrally generate game maps

Alex 8 aylar önce

I've been reading 'The Second Kind of Impossible', it's really good.

EHH246 4 aylar önce

My question were there any designers looking at these patterns and going "I know what my next floor is going to look like"?

Kaththee 2 aylar önce

My ADD took me from tempering chocolate (melting and cooling chocolate so it sets up and is stable) to this fascinating video which I had to pause and rewind several times just to follow. Not to mention all the times I had to stop the video a few times to look things up like "icosahedrons" to "vertices." This is why I never get anything done.

Lmjacks Yıl önce

I love everything about this, it’s so satisfying in so many ways-this is incredible, thank you for talking about it

NYANUAR Yıl önce

HEHEHE I AM A SUPAHSTAR CLOD yes

HEHEHE I AM A SUPAHSTAR CLOD Yıl önce

a fellow mountain climber, I see

Semaj_502 Yıl önce

Right? Normally high level stuff like this makes no sense to me, but this did and in like a really beautiful way

Steve Thea Yıl önce

@Kataiser i want to report my payment on 29th, i did not see bill come so i checked it's overdue i dont want to be stung late fee plz

NYANUAR Yıl önce

c e l e s t from m a d e l I n e

Daniel Ene 12 gün önce

What's interesting here is that fractals are infinite patterns that always repeats. But this is an infinite pattern that never repeats exactly. Which is kind of amazing. It's much like our universe

Xiao 5 aylar önce

@2:05 My high school teacher taught us how to calculate the maximum number of balls that a cylinder could hold using the same arrangement. I was thinking why this gives us the maximum number? The proof was published in 2017... with so many authors on it.

Luis ER 8 aylar önce

10:59 this reminds me of fractals and their strange infinite patterns

Rick and Rygel 2 aylar önce

So if the golden ratio makes infinite non repeating patterns, and the universe is full of the golden ratio, then wouldn't it follow logically that even if the universe is infinite there would never be a repeat earth or other versions of people or even other humans?

Miłosz Masłyk 2 aylar önce

Nono, there will never be an earth that is the *exact same* as ours

Abhishek shah Yıl önce

I love how Veritasium has transitioned from physics into geometry, chaos theory and more math topics. Would love to see him cover some of graph theory as well!

Andras D. Nagy Yıl önce

@Ruben Alba ;)

Ruben Alba Yıl önce

@Andras D. Nagy don't feed the troll

Alethia Krino Yıl önce

also philosophy at the end when he questions if there are nonexistent things

רותם שלו Yıl önce

I mean, these are all things that were briefly discussed in my physics BA, but yeah they're mostly math-y

Sagittarius A* 2 aylar önce

So interestig! What an achievement of Penrose to reduce the shapes to two and that the pattern matches Kepler's 400 years old one - incredible.

Dustin Jacobsen 2 aylar önce

I'm amazed that you or your tech team found a way to demonstrate a Moiré in a TRvid video. Did you do any processing to avoid getting Moirés with the grid of pixels? Did compression give you any trouble?

UranusProductions1 4 aylar önce

Yeah we're definitely in a simulation bc this is all lining up too perfectly

Thomas Ngeow 3 aylar önce

He stumbled on the true nature of reality at 12:15: "Where there is an uncountable infinity of different Universes, but just by looking at them, you could never tell them apart." Amazing!

carykh Yıl önce

Whoa, the animations at 7:30 really helped me understand Penrose tiling better than anything I've seen before :O

Map 4 aylar önce

cary kepler hatchet

Map 4 aylar önce

cary killing hater

Tabla Sechstitu Yıl önce

Hi

Japan Ball 2 aylar önce

1:24: "There are just five platonic solids." Pentagonal Trapezohedrons: Am I a joke to you?

Japan Ball 29 gün önce

@Arturo’s Michelangeli Maybe it's because some pieces are upside down.

Arturo’s Michelangeli Aylar önce

The pentagonal trapezohedron is not a joke to me! Unfortunately, however it’s a “regular solid”, not a Platonic solid. boo!

musikali1 3 aylar önce

Excellent video!! Small remark: the 5-squeezing in 13:08 is kinda cheap. 0.5 is just 1/2, has NOTHING to do with 5, it's arbitrary just as base 10, and you know it.

Dimitri Isov 3 aylar önce

When he revealed the golden ratio is at the center of all this I felt the cosmos align.

Sunny🌿 4 aylar önce

I'm noticing that anything that's mathematical and extremely fascinating to me is almost guaranteed to involve the Golden Ratio and Fibonacci sequence

jmir Yıl önce

The madlad actually made this video's aspect ratio the golden ratio :D I was so confused until I divided the pixels after watching the video. Nice touch 👍

Sreenikethan I Yıl önce

@Robert S. IKR

Robert S. Yıl önce

I just noticed the same thing right before I saw your comment, it's so subtle but I love it

Sylvain S. Yıl önce

THEORIA OMNIA est un chercheur indépendant qui a développé une théorie qui va beaucoup plus loin que ce qui est montré ici... Faites une recherche...

Sreenikethan I Yıl önce

Can confirm

SupermassiveBlackHole 3 aylar önce

The math nerd in me: wow, that's absolutely fascinating, id like to study it further The art nerd in me: make a quilt

Ali Ghadamyari 7 aylar önce

wow. it's mind-blowing! really fascinated me!

Isaac Kellar 5 aylar önce

How do you find, and cram, so much info into one video… and somehow in an understandable way…

Vec Benoit 2 aylar önce

Totally fascinating. Thank you.

Z TPI Yıl önce

Me: Gives this pattern to the guy tiling my kitchen Tile guy: Sweats profusely

Raymond Myers Yıl önce

Teacher: “What’s on your mind?” My Mind:

Ignacio D Yıl önce

At least my avatar is relevant 😄

FacelessForever Yıl önce

better yet, hand him the pattern. give him the two distinct pieces and tell him to "make it happen"

Tony Fisher Yıl önce

It's the exact opposite of a pattern.

Peter Bennett 8 aylar önce

Great video. Enjoyed it - thanks

Lucas Walters 5 aylar önce

This channel is nerd heaven and I’m obsessed with it. Never cease to learn new things

ThatFamiIiarNight 6 aylar önce

1:27 yes, there are 5 platonic solids. there are not 5 regular polyhedra. there are 48.

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