5 and Penrose Tiling - Numberphile

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Why five-sided figures pose a problem from Professor John Hunton - and a bit about the importance of Penrose Tiling.
More links & stuff in full description below ↓↓↓
Professor Hunton works at the University of Leicester.
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15 июн 2024

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Комментарии : 495

@MaestroAlvis 12 лет назад

"The important thing about 5 is that it's not 3, 4, or 6." I often find myself explaining mathematical concepts and pretty much the stuff on this channel, to my friends. I'm going to start using this quote because more then once have I been asked why 5.

@linkVIII 9 лет назад

"Science can't see what it doesn't have the language to describe" What a great quote.

@naimulhaq9626 9 лет назад

It is extremely surprising that the 'language' found by the Nobel Lauriet, could 'describe', infinite variety

@RalphDratman 8 лет назад

+linkviii To establish or refute that assertion, one would have to perform experiments on groups of scientists. The scientists would be asked to solve novel problems for which their language was or was not compatible with the task. However, the test makers would need to have the language to describe the tasks.

@ragnkja 7 лет назад

You'll never notice something you had no idea you could look for.

@hankroest6836 7 лет назад

It's like the old line: We don't know who discovered water but we know it wasn't a fish.

@Akash_Tyagi_93 6 лет назад

Totally right. One similar example is- If we listen to a language that we don't know anything about, then we won't really "hear" it no matter how hard we try.

@pratikmaitra8543 3 года назад

Now he has won the Nobel prize.

@kunaldhawan5952 3 года назад

Yep yep great diverse guy

@M.-.D 3 года назад

So incredible to see Professor Penrose win the Nobel Prize. One of the greatest minds.

@kevinohare9216 Год назад

And of course this video refers to Schectman winning one too. Pretty cool that laureates in Physics and Chemistry, respectively, both touched on these mathematical concepts.

@jursamaj 5 месяцев назад

Too bad he now suffers from Nobel disease…

@TheLoquid 12 лет назад

I love the observation about language as a limiting factor for thought. That particular idea is one of my favorite philosophical issues.

@MemoryCardOfLife 12 лет назад

"Science can't see what it doesn't have the language to describe." Such a good quote.

@numberphile 12 лет назад

good to hear - more to come!

@RC_Engineering Год назад

Cant wait to see the follow up on the new 13 sided shape that tiles the plane without repeating!

@pizzarella985 7 лет назад

AAAH, SO THIS IS THE WAY I SHOULD TO PLACE THESE SQUARE TILES, THANK YOU

@tjdonald9084 3 года назад

This is the best explanation for penrose tiling. The ending segment blew my mind

@yobar23 12 лет назад

I love that last sentence! "Science can't see what it doesn't have the language to describe."

@jbsoul4575 4 года назад

I read an interesting article in "Scientific American" back in the 80's. Titled something like, "Symmetry in Chaos." Found it quite interesting even though I have a high school education. It was specifically about Penrose tiling.

@amoeba80 11 лет назад

he has an appealing accent... he can talk for hours and I won't get bored!

@amazingpie8 12 лет назад

Im 18 and I'm a pretty well balanced kid when it comes to school, sports, and social life....but these videos just let me embrace my inner nerd and i love it

@lydianlights 12 лет назад

Wow, I've never head of this before. That's pretty awesome!

@DarkenedYeastExtract 12 лет назад

This feels like a TED talk version of Vihart. That by no means is a criticism! This is really awesome.

@RobotProctor 4 года назад

"We didn't see it because we didn't look for it" Happy searching, people

@jonabirdd 10 лет назад

wow the part at the end was pretty profound!

@theRealPlaidRabbit 10 лет назад

The very first sentence was the one that got me. Although I found the last intriguing as well.

@jamma246 12 лет назад

By "repeat" here, he means that any local patterns can be seen infinitely often and regularly - more precisely, for any sized patch of tiles you want, there is another radius such that that pattern can be found in the tiling to within that radius of any point in the tiling. This is an amazing property and in some way generalises the usual periodic patterns (periodic means I can pick up the tiling, move it, and it looks the same again - this isn't the case for the Penrose tilings).

@Ressilge 12 лет назад

This is by far one of your best videos, I loved it so much :D

@5Davideo 11 лет назад

I remember playing with a set tiles as a kid. There were hexagons, triangles, squares, trapezoids, and two rhombuses. It was really fun to put them together in different patterns and tilings. Maybe one day I'll pass it on to my kids, and I'll add some more pieces derived from pentagons for even more variety.

@StephRenee812 Год назад

I'm trying to draw up my own patterns to make templates for a quilt I want to make..

@DaithiDublin 12 лет назад

I've been tiling for about 7 years now and I would bloody love to be asked to do a Penrose pattern! I've never even seen such tiles on sale anywhere. Victorian geometric patterns are close, but that floor at 5:13 looks amazing! I'd love to know where it is.

@Chrisklown 8 месяцев назад

Google: The University of Western Australia - Bayliss Building

@ObjectsInMotion 11 лет назад

If you were subscribed to brady's other channels, you would see why they tie their videos to a number. This channel is supposed to be a collection of videos about the numbers in our daily lives, while sneaking in advanced mathematical concepts, like sixtysymbols is a collection of symbols, but really about physics, and periodicvideos is a collection of elements, but you also learn a lot about chemistry.

@rauc6788 12 лет назад

Wonderful video again. Really rich in content and food for thought on many levels by using one central example and several nice anecdotes. Excellent job Brady. I have always loved the fact that humans are so linked to experience and perception and how culture, language and experience can so affect the outcome of an event.

@EPMTUNES 2 года назад

I agree! Massively interesting video!

@Bresixdouze 11 лет назад

Epic quote. This is what stood out most to me, as well.

@PianoMan347 11 лет назад

Thank you for using a sharpie instead of those other painfully squeaky markers that they normally use on this channel.

@numberphile 12 лет назад

Thank you!

@numberphile 12 лет назад

@Thegeeksquadofone thank you... we're really enjoying it too.

@kevin9794 11 лет назад

Indeed. That's probably why they have proved so crucial in the development of so many fundamental sciences! :)

@numberphile 12 лет назад

@TomatoBreadOrgasm Professor Hunton is from the University of Leicester! And my motives are pure!

@6reve 12 лет назад

Ever since I read about penrose tiling, I've hoped I got the chance to use it in practice. Thanks for the video!

@painxtreme 11 лет назад

Brady, one thing overlooked in this one, that I can see 1st hand. I am pretty sure that quilters have been overcoming these angular difficulties with repeating, fill in shapes, farther back than the 1980s, and possibly the 1880s. Just do a simple google search of geometric quilts, and I would bet you'll find this problem has been tackled by hobbyists, my Grandmom, Wife, and a plethora of others, for quite some time....Just an interesting aside. Thanks for all your videos, they are brain candy :)

@JuddNiemann 11 лет назад

This was a really great episode.

@ltviktor 11 лет назад

Brady (the editor) saying with enlightment: "Aaaaah... ah!

@witchdoctor94 12 лет назад

I get a big smile when i see my sub box and you guys uploaded a video

@LudwigSpiegel 12 лет назад

Thank you! I enjoyed this video very much..... keep up the good work!

@drakzov 12 лет назад

Thank you Brady! You're awesome!

@m4rcos_elx95 2 года назад

The best videos of the world. thanks Brad.

@ShakaLakaMTB 12 лет назад

I really like your work. Thank you!!!

@mimicici13 12 лет назад

I tend to become mesmerized by tile patterns. This was really interesting!

@numberphile 12 лет назад

@mimicici13 glad you liked it!

@numberphile 12 лет назад

pleased to be of service

@MrJepcats 12 лет назад

One of my favourite numberphile videos so far. You guys should do a video on infinity :)

@HeyJD123 12 лет назад

Great video. It seems like this knowledge will be of use to me.

@NeverMindSophie 12 лет назад

Ah Brady you do such a great job.

@keniangervo8417 11 лет назад

"Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing." Check "Sphere Packing" from Wikipedia.

@StephenTack 9 лет назад

"Science can't see what it doesn't have the language to describe."

@EquitoErgoSum 12 лет назад

@numberphile AH, I missed that. Thanks! I've just discovered your channel. It's great.

@ragnkja 10 лет назад

The question at the end is very interesting, and the conclusion that you can't see something you didn't know you could be looking for is even more interesting, particularly for those of us who intend to become professional scientists.

@Romik2508 12 лет назад

@numberphile maybe because so much in my life is associated with this number. This, of course, can be said about any number. But 5 seems to me very beautiful. It is easy to count something using 5 (well, for me personally) when you do exercise, for example. Also in Kazakhstan, where I come from, 5 is the highest mark in school, so all students want and like this number)) I just love it. Hope I'm not alone. Thank you again))

@lavanya2world 12 лет назад

very interesting information

@grande1899 12 лет назад

@Bugside That pattern will not tile well in a flat plane though.

@xxfazenoscoper360doesnosco7 3 года назад

YOOO WTF IS THIS GRANDAYY

@godrequiem5014 3 года назад

@@xxfazenoscoper360doesnosco7 yo

@earth11116 3 года назад

Wtf lol

@Villex93 12 лет назад

Thanks for the answer!

@lucashoffses9019 8 лет назад

2:22 WHAT WAS THAT STRANGE NOISE!!! IT SOUNDS WEIRDER THAN A MINECRAFT VILLAGER!

@whitherwhence 8 лет назад

IT SOUNDS LIKE A PEACOCK WITH A NASAL INFECTION!

@thatoneguy9582 8 лет назад

murr

@carelia7868 8 лет назад

oh yeah mb i thought about it like 6 hexagons together but it does not make a 36gon i went to fast >

@totaltotalmonkey 6 лет назад

It is a sheep making the noise.

@goose300183 5 лет назад

It was Brady's dramatic realisation that everything he thought he knew was a lie.

@ruaridhdon 12 лет назад

This is like the shapes that make up a football. I've always wondered why they don't just use pentagons all over, NOW I KNOW!!

@NagisaOfficial_0v3rachi3v3r 12 лет назад

We just talked about this in geometry. Thanks for the pre-lesson so I sound smart compared to others :)

@TheBagleboy 11 лет назад

Its at a university in my city and basically the first thing you get told about the building is that there is one point, where no matter where you look it is identical on all sides.

@miz8us 12 лет назад

Great vid! Thanks :)

@N3bu14Gr4y 11 лет назад

As long as your symbols don't resemble each other when written in a line of condensed text, you can use as high a base as desired. You could even encode the symbol's value into its structure. For base 32, you could have symbols consisting of vertical lines with up to five short horizontal lines jutting out from them. To avoid confusion with the middle bars, special accents can distinguish them in the digits where their neighbors are absent. One could use this method for other bases as well.

@KairuHakubi 10 лет назад

i run into this whenever i try to draw a tortoise shell their shell scutes are inexorably pentagonal, but they don't tesselate properly

@LTC3a 11 лет назад

Glad to help!

@Romik2508 12 лет назад

5 is my favorite number. thank you for video))

@helenadrugo4337 3 года назад

Amazing vid!! Thinking of painting it in my bedroom wall :))

@Thegeeksquadofone 12 лет назад

Your channel is awesome!!! :D

@Tupster 11 лет назад

Yes, I am subscribed to the other channels. I think we both agree that the format can be a little limiting. Form is liberating, but sometimes it feels a little artificial. If we agree on anything I think it is that. We just want different things and there's nothing wrong with that.

@numberphile 12 лет назад

We will!

@drawwithtina7951 9 лет назад

The building featured at 5:20 - is it the Bayliss Building at the University of Western Australia, or a different one?

@TdyBear 12 лет назад

I love all these videos, shame there wasn't some sort of explanation as to how some Penrose patterns are formed, I just like equations that explain things.

@HallowedError 11 лет назад

This dude kept reminding me of Nigel Thornberry. It's awesome!

@Gullshunter 12 лет назад

loved this video :) don't forget you told me you were going to talk about the Graham number :)

@lmaso99xx 12 лет назад

great video :)

@raykent3211 8 лет назад

nice video. For once, I think I understood what a mathematician was saying! Some viewer confusion could have been avoided if he'd sayed "plane" means flat surface, repeat flat. And the challenge is to find the minimum set of different tiles including a regular pentagon that might be mass-produced. Did he get it down to 5? The idea of "never repeats" is worthy of a few more words. Penrose's hour long lecture is very enjoyable. I think he was 80 or 90 years old and bright as a button. And witty.

@sniggleboots 7 лет назад

I agree that for the curious mind, Prof. Hunton's explanation is deeply unsatisfying. Do you happen to have a source of a more in-depth explanation? I admit I don't want to watch an hour long video and end up none the wiser afterwards.

@raykent3211 7 лет назад

Sorry, I can't help, I've only dipped a toe in the water myself. It's interesting that Escher tiled a pseudo-spherical surface with fewer shapes... birds? ... lizards? ... I forget, but you can see those on google images if you're interested.

@sniggleboots 7 лет назад

Ray Kent alright, no worries, thanks anyway!

@gocoady6717 7 лет назад

Ray Kent m

@lapkamil 12 лет назад

thank you

@DRD363 8 лет назад

this is my favorite

@numberphile 12 лет назад

@Romik2508 cool... why 5 I wonder?

@CreeperInWaiting 12 лет назад

5 is my lucky number!!! It's crazy that it is this special.

@Nathan8885 10 лет назад

We can also see this in viruses with icosahedral capsids. The most obvious is the dodecahedron structure with pentagonal faces. I think it's likely that they are structured this way so that the capsid can form a closed unit since it can't tile.

@numberphile 12 лет назад

@EquitoErgoSum I've posted the periodicvideos film about quaiscrystals and Nobel Prize as a video response

@mokopa 12 лет назад

Just as a matter of observational curiosity...there appears to be a few striking similarities between Professor John Hunton's delivery and that of Professor Mike Merrifield (DeepSkyVideos). They have very much the same facial expressions (for example, emphasis of important facts with a raising of the eyebrows), conversational cadence, tone and gestures. :)

@AlanKey86 12 лет назад

@Ypthor Yes. Consider the outline of a house (square box with triangular roof)

@instormental 11 лет назад

How about tiling with non-equal sided pentagons? Is there a pentagon with particular proportions of side lengths/angles that you can use to tile, without using any other shapes? Or maybe you can use a shape with the same angles but different size (I see it still wouldn't work with equal-sided pentagons but what about non-equal sided?)

@Tupster 11 лет назад

Of course they can do whatever they want, but my opinion is that although numbers are fascinating I'd like to hear these same people talk about mathematical ideas without having to tie it to a specific number. Math is so much more. If this series is supposed to be mostly about theoretically unimportant number games than that is fine, but I think they want to do more.

@bizlur 12 лет назад

If I ever have to retile a bathroom... it must be a Penrose pattern! this is awesome.

@markhughes7927 6 лет назад

The artist M.C.Escher was doing experiments with these principles in the 3rd, 4th, 5th, and 6th decades of the 20th.century. The geometer Coxeter - even earlier, as also, in a rather different way - Richard Buckminster Fuller.

@shugaroony 5 лет назад

Penrose loved Escher and I think met up with him to discuss his work and think Escher made a drawing for him.

@knightriderultimate 11 лет назад

wow, well said

@NoriMori1992 8 лет назад

Today I learned that Prof. John Hunton is really bad at drawing pentagons. XD

@danpal6737 3 года назад

nah kusai nori mori

@Qaptyl 3 года назад

lol cairo tile

@OnlyARide 11 лет назад

Please do a video on fractals!

@guycomments 10 лет назад

Mr. Hunton has a fantastic voice

@kalmdwn7711 3 года назад

Instructions to renovation company: Pentagon tiles, no gaps

@randywebb8284 3 года назад

Squares.... "non-repeating, tiled".

@juanausensi499 3 года назад

@@randywebb8284 It's possible to do a non-repeating square tiling. Do the first row the standard way. Then, displace the row above that row a little bit. Then, displace the next row 2 times that bit. Rinse and repeat. If this bit is not a rational number (based on the tile square lenght), you have a non-repeating square tiling.

@bennettwildfire 12 лет назад

05:14 This is the floor of the Bayliss Building (renamed Molecular & Chemical Science Building) at University of Western Australia. Before seeing the video we spent ages training to find a line of symmetry somewhere.

@NathanClingan 11 лет назад

Who first discovered Penrose tiling in nature? It must have been the most thrilling moment of his life.

@sethyboy0 11 лет назад

Keep doing 2:21 over and over again and it sounds like a goat XD

@yaerius 11 лет назад

you can mix 8-sided with squares, it looks quite nice :)

@theeclipsemaster 2 года назад

Yes but this is more fun

@NoriMori1992 8 лет назад

3:58 - Wow! These patterns remind me a lot of the game CirKis! Especially the ones with several colours!

@jursamaj 5 лет назад

That's because CirKis was explicitly based on Penrose tiling.

@TVjoakim 12 лет назад

I'm not so good at math at shcool, but i really enjoy your videos :)

@numberphile 12 лет назад

you probably are!

@christronomatic 12 лет назад

interesting! It's almost as if no matter how complicated something might seem, theres always a pattern somewhere within

@michaelbauers8800 9 лет назад

Wasn't there an example of aperiodic tiling similar to Penrose in some ancient architectural feature? Islamic?

@missingno9 8 лет назад

+Michael Bauers Yeah, something about "Girih tiles"

@BauthorFowler 3 года назад

But were the tiles in the Islamic example equilateral?

@LTC3a 11 лет назад

In order to tile there is a min of 3 shapes at a junction. If they were regular polygons, the total angle size would be bigger than 360 degrees. 6 is the biggest because each angle is 120 degrees * 3 = 360.