With these numberphile vids and their random examples it always makes me wonder if they just don't prepare at all or if they're simply autistic (nothing against autism, it's a perfectly beautiful state of being)
@@jeupater1429 many brilliant minds fall somewhere on the spectrum! Also, studies have shown that children of high-IQ individuals are more likely to be on the spectrum - especially high-IQ scientists and mathematicians. Not saying Tadashi Tokieda is on the spectrum. I just find these facts interesting.
I'm a gate and fence manufacturer.. we got sheets of circular perforated sheets in a hexagonal pattern to clad some fences shortly after seeing this vid.. the offcuts were just thrown on the bench randomly (as you do), and I noticed the larger hexagonal pattern just walking by one day, so started playing with it (and of course showing my work-mates / boss). my fav effect was a whole heap on top of each other (could see the effect more clearly), and with the top 4 sheets, you make it so the top one makes really big circles with the 2nd sheet, and the 3rd sheet makes somewhat smaller circles with the 4th sheet.. you can only see the small circles that the 3rd makes with the 4th through the big circles that the 1st makes with the 2nd. Outside of the bigger circles (from the 1st and 2nd), you can't see the smaller circles ..very cool
Awesome. You need to deal with this effect a lot in commercial printing. Since 4-color CMYK images are printed using grids of dots, if you just overlay all 4 grids at the same angle then the slightest offset will create Moire patterns. So you have to make the angle between the grids for each color maximally separated (at around 30 degrees), which makes very tiny "rosette" patterns that you can see if you look closely at a printed package.
6:22 his "just" doesn't refer to inifinity at all, but is rather used as "recently". Technically, you didn't say any different, and it feels like I just got clickbaited by a comment. Weird.
One can think that this is just mathematical ramblings, but this same Moire Pattern is present in graphene layers, and is a whole new study field in physics and chemistry.
+Luke Whelan Not even an hour, if I try to select anything more then 480p it will buffer over and over again for 20 minutes then will just stop with an error. Even in shitty resolution this was still an interesting video.
Tadashi Tokieda is awesome. I HIGHLY encourage people to watch his talk "Math Encounters -- Toy Models: Extracting Mathematical Surprises from Everyday Life", also found on RUclips.
Great video. What i like about the videos with Tadashi Tokieda is the simplicity. I mean i could listen to Phil Moriarty talking about Entropy and Ed Copeland talking Dark-Quantum-String-weirdness all day, but i seriously like the style of his (Tadashi Tokieda) videos.
I think this is a great maths video, because it is not overly directed. Many maths videos are strongly directed, meaning that they pose a single, very specific goal, and then work solely towards that goal. That's okay, but it is important to also have these videos which are not so directed at a specific goal; they tend to be more broadly approachable and more involving. Sugoi!
Yes! A new numberphile video! I was checking youtube constantly for updates. Amazing video as always! This channel makes me appreciate mathematics soo much more. Thank you!
Wow. Even as I child I was always curious about these types of patterns that emerge when you look through things like a meshed square trash bin. FINALLY someone showed me how this actually happens. Thank you!
i have noticed something. mathematicians are much more charming than physics on the brady's videos. they are very into the subject, very modest, never condescending, never smug...
+T. Markus Gellert "If you think maths is only about numbers, then you must think that Shakespeare is just about letters." -The eccentric man from the glass Klein Bottle episode
Man, I love this guy's accent... he speaks perfect English but with a cultured, educated Japanese accent that is instantly recognisable and distinctive.
I am really, really, liking this professor. The paper tricks were great, and now? He's doing this sitting on the floor! This is the kind of a person that grabs the imagination of kids, which means they just may learn something.
+j0nthegreat I mean, it sort of makes sense. If you have a plane with an object on it, and rotate the plane relative to a point somewhere on the plane, then the object moves along the border of the circle of a radius equal to the lenght of the distance between the center of rotation and the object in question. So the longer the distance, the longer the border, and thus the trajectory of the object becomes straighter. Thus if the center is at infinity, the distance between the center and the object is infinite, and thus the radius of the circle is infinite, which means that the trajectory is a straight line. Simply put, as the distance between the object and the center of rotation approaches infinity, its movement trajectory during the rotation approaches a straight line.
+ComputersAreRealCool It wasn't so bad at my end... But yes, since you're imposing a regular grid (cells in the sensor and pixels in the video) onto this grid yet again, the effect will suffer. Same if you scan or even re-print an image printed with offset-print, for example. You can see the Moiré effect happening between printed dots and cells/pixels at 3:45 quite well :) That time, the undesired effect can be used to illustrate the contents of the video :D And with compression, there are different techniques, but many divide the picture up into fields of 8x8 pixels, for example.
Such an easy lab/demo that you can give to kids in class. I hope there's teachers out there watching this so one lucky classroom can have their minds blown as much as we did!
This guy is awesome! I'd love to see more of his demonstrations! Those demonstrations sort of reminded me of isomeric compounds rotating polarized light clockwise (dextrorotatory) and (levorotatory) anticlockwise! That's so cool!
That's awesome. It actually answers a question I've had since I was young - why you get concentric circles when you look at a street lamp through the branches of a tree without leaves... Thanks!
+Minihood31770 Yeah that's the problem (though you could certainly make patterns with them anyway) that you can't tile a plane using other regular shapes than squares, triangles and hexagons. BUT you could take weird irregular shapes and make stuff, or patterns of dots, the only problem is that you kinda need the pattern to have some manner of rotational symmetry for at least the moiré patterns to emerge :)
+Minihood31770 I was testing something similar to this a few weeks ago, although I used hexagons. If you rotate the top layer to the correct angle, you can see 6 pointed stars emerge. I imagine you'd get 5 pointed stars from tesselating pentagons.
One can think of the transparency as a sampling pattern and the paper some signals. Plotting the patterns in the Frouier domain may explain the phenomenon more clearly.
Moire patterns appeared in my research on lattices in Bose-Einstein condensates, with a manuscript on the topic gone for peer review (browse playlists if you'd like to see). They are beautiful. Oh, and nice work!
even without numbers it is still math -- this is symmetry and euclidean transformation, just not quantized. He at least points out that triangular lattices are symmetric with 120 degree rotations xD and also introduces the concept of duals, which is big in geometry and group theory.
Just a regular troll, I find it quite funny, sometimes. Somewhere in the world, a dude is spreading "yes" and "no" on a math channel. But you know, I'm not Dr. House, so maybe I'm a moron too, hahahaha . (Sorry for my bad english)
+Migas Almeida Only for the first half minute though. XD And one of his legs was lying on the chair sideways under him, rather than both knees up to his chest. XD
I found that while I was playing with perfboard PCB, these are boards with array of drills. Once I placed hole above hole in both noting appeared but once I rotated one the same pattern emerged, array of circles that grow or get smaller :)
![Seungmin "그렇게, 천천히, 우리(As we are)" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/kAzmhLHePqU/mqdefault.jpg)
I like how he has a knife and a block of wood, as opposed to, say, a couple of rulers.
What, you mean you don't usually carry a knife and a block of wood?
With these numberphile vids and their random examples it always makes me wonder if they just don't prepare at all or if they're simply autistic (nothing against autism, it's a perfectly beautiful state of being)
@@jeupater1429 many brilliant minds fall somewhere on the spectrum! Also, studies have shown that children of high-IQ individuals are more likely to be on the spectrum - especially high-IQ scientists and mathematicians.
Not saying Tadashi Tokieda is on the spectrum. I just find these facts interesting.
@Reunite The British Empire Those studies aren't all that exact.
@@lostindixie I never said they were exact, I said they show a correlation. More research is definitely needed to say anything more about this topic.
"translations are just rotations with the center at infinity" - he said it only briefly, but I just had my mind blown xD
+some1rational 0:54
+some1rational thank you I was distracted and missed this; you've made the risky choice of reading comments completely worthwhile.
than this would make rotations a sum of infinitesimal translations...
@@theodorostsilikis4025
Yes. You can measure the circumference of a circle with an infinitesimal ruler.
Bernard Riemann: "Yep"
I'm a gate and fence manufacturer..
we got sheets of circular perforated sheets in a hexagonal pattern to clad some fences shortly after seeing this vid..
the offcuts were just thrown on the bench randomly (as you do), and I noticed the larger hexagonal pattern just walking by one day, so started playing with it (and of course showing my work-mates / boss).
my fav effect was a whole heap on top of each other (could see the effect more clearly), and with the top 4 sheets, you make it so the top one makes really big circles with the 2nd sheet, and the 3rd sheet makes somewhat smaller circles with the 4th sheet..
you can only see the small circles that the 3rd makes with the 4th through the big circles that the 1st makes with the 2nd. Outside of the bigger circles (from the 1st and 2nd), you can't see the smaller circles
..very cool
no wonder my fence is taking so long to be built
Where can i see this?!
Professor "The photocopier is out of paper!"
Faculty assistant: "I just refilled it yesterday."
Professor : "Tadashi must be back from his sabbatical"
beats being out of shared computer time!
This explains the patterns I've been seeing all my life when two mosquito screen door overlap each others. Thanks!
Me too, always wondered.
[Insert 'Confused Tom' Meme]
or in the electric fan when blades are removed
Its called moiree pattern
When a grid’s misaligned,
With another behind,
That’s a moiré.
~xkcd
when the spacing is tight,
and the difference is slight,
that's a moiré.
😂
Ahaha
now I want a pizza
You should win the Best Comment Award.
this man's clarity of thought and speech is extremely impressive.. exceptional.
And he's using a second (at least) language too!
Exactly what I came to say. Not a wasted word or incomplete thought in any of his utterances
He makes toys and puzzles as a career. Very interesting man.
"translation is like rotation with the center at infinity."
How have I never heard this before? Mindblow.
Oh god, my eyes when the non-random spectrum started.
+StormGaming
Yes
+StormGaming Yes
+StormGaming
Yes
+Shilag My brain!
same
This guy is awesome! Please do more videos with Tadashi!
+Brandon Butler So much this! He bends my mind in such a delightful way!
+Brandon Butler All the yes!
+Brandon Butler Not as awesome as Cliff Stoll. Have you seen the klein bottle video?
***** Yes, I like this guy better. I wouldn't be afraid of taking a class with Tadashi ;)
Brandon Butler Well, I respect your opinion.
Awesome. You need to deal with this effect a lot in commercial printing. Since 4-color CMYK images are printed using grids of dots, if you just overlay all 4 grids at the same angle then the slightest offset will create Moire patterns. So you have to make the angle between the grids for each color maximally separated (at around 30 degrees), which makes very tiny "rosette" patterns that you can see if you look closely at a printed package.
Very cool! Thanks for sharing!
Only a mathematician will use the words “just” and “infinity” in the same sentence
Here was not complicated infinity, another one can be much more complicated. So, just easy infinity.
6:22 his "just" doesn't refer to inifinity at all, but is rather used as "recently".
Technically, you didn't say any different, and it feels like I just got clickbaited by a comment. Weird.
"I just thought it would be a quick stroll, until he dragged me along to the edge of infinity!"
Tadashi you are blowing my mind,
This man is great! I like the topic he chooses and his overall style.
Merry christmas to all numberphiles!
Damn my eyes hurt
+StormGaming
Yes
+StormGaming Yes
+TheShadowKitana But its still worth watcing.
+StormGaming
Yes
+tothfirytoob My man!
One can think that this is just mathematical ramblings, but this same Moire Pattern is present in graphene layers, and is a whole new study field in physics and chemistry.
RUclips compression doesn't like this ;p
+Joof
RUclips "I hate randomness.".
+StormGaming
Yes
+StormGaming Yes
+StormGaming
Yes
+tothfirytoob My man!
moire patterns go very well with video compression, not.
+ollj oh definitely up your RUclips setting to HD if you are not already!
+Numberphile Okey dokey, I'll be back in an hour!
+Numberphile I want to see this kind of thing in 4k. On second thought, I could just see it in real life. Hmm...
+Luke Whelan Not even an hour, if I try to select anything more then 480p it will buffer over and over again for 20 minutes then will just stop with an error.
Even in shitty resolution this was still an interesting video.
+TheD1ddler I get 1080p. You may need to take action of some kind.
Tadashi Tokieda is awesome. I HIGHLY encourage people to watch his talk "Math Encounters -- Toy Models: Extracting Mathematical Surprises from Everyday Life", also found on RUclips.
He is also a polyglot.
I can honestly say this was probably the coolest thing I've ever seen on RUclips
"...the result is interestingly boring..." I laughed so hard! xD
Great video. What i like about the videos with Tadashi Tokieda is the simplicity. I mean i could listen to Phil Moriarty talking about Entropy and Ed Copeland talking Dark-Quantum-String-weirdness all day, but i seriously like the style of his (Tadashi Tokieda) videos.
That's it?! This video could be 30 minutes longer! =P
+StormGaming
Yes
+StormGaming Yes
+StormGaming yes
vavanade I wish. If only there was additional footage.
+vavanade Or an infinitely long livestream.
This guy blows my mind! Definitely a new Numberphile fave. Looking forward to more videos with Tadashi!
OMG its the foot guy!!!!
+Fed480 what are you referring to?
+Terry Martin One of the Mobius strip videos
+Terry Martin ruclips.net/video/F-TJfqN_HC0/видео.html
+StormGaming
Yes
+StormGaming Yes
I'd like to thank you for the captions, because sometimes I struggle to understand people's accents. Lovely video.
i wonder how much larger this video file was than a normal video of the same length
+StormGaming
Yes
Still smaller than your mom
+StormGaming Yes
+StormGaming Yes
+StormGaming Yes
I think this is a great maths video, because it is not overly directed. Many maths videos are strongly directed, meaning that they pose a single, very specific goal, and then work solely towards that goal. That's okay, but it is important to also have these videos which are not so directed at a specific goal; they tend to be more broadly approachable and more involving. Sugoi!
4:50 I love the effect that's produced from him accidentally warping the transparency
Yes! A new numberphile video! I was checking youtube constantly for updates. Amazing video as always! This channel makes me appreciate mathematics soo much more. Thank you!
Totally had to make some patterns in autocad and print them out on vellum paper. So much fun to play with!
Wow. Even as I child I was always curious about these types of patterns that emerge when you look through things like a meshed square trash bin. FINALLY someone showed me how this actually happens. Thank you!
i have noticed something. mathematicians are much more charming than physics on the brady's videos. they are very into the subject, very modest, never condescending, never smug...
Cause mathematics includes assumptions and physics is the opposite of assumptions. Assumptions are always fascinating.
This man is the most wonderful explicator of concepts you have yet had on this channel. Top marks!
Numberphile 2012: Let's talk about special numbers!
Numberphile 2015: Let's play with paper and transparencies!
Maths will always be maths
+Jay Eki Except when you're in the USA ;-0
+T. Markus Gellert "If you think maths is only about numbers, then you must think that Shakespeare is just about letters."
-The eccentric man from the glass Klein Bottle episode
Jacob Raymond
Cliff may be right but this is still NUMBERphile. Also he said "words", not "letters".
+T. Markus Gellert Well, after the infinity videos they kinda ran outta numbers.
Tadashi's videos so far have been some of my favorite numberphile videos to date!
The asmr is strong in this man
I like this! Thanks for coming back, Mr Tokieda!
Or rather, Mr. Tadashi
Man, I love this guy's accent... he speaks perfect English but with a cultured, educated Japanese accent that is instantly recognisable and distinctive.
He is a polyglot.
Waked and baked and watched this. Best start to my day. Great visuals
wait.. translation is just rotation with the center at infinity... mind blown.
love everything this guy does - his popular lectures for the LMS and IMA are amazing!
I get hella ASMR from Tokieda's voice.
+meadslosh same here. Also, he always shows some very interesting stuff.
without a doubt, my favourite numerphile presentor :) just the best :)
Woops found the shape of the fabric of reality with two sheets of paper
I am really, really, liking this professor. The paper tricks were great, and now? He's doing this sitting on the floor! This is the kind of a person that grabs the imagination of kids, which means they just may learn something.
I gazed into the abyss, and the abyss gazes also into me.
This man is an awesome teacher, and he is very soothing to listen to. I hope there are lots more videos with him!
a translation is a rotation with the center at infinity??? whaaaaa???
+Bluelightzero hmmm, i suppose so. thanks.
+j0nthegreat I mean, it sort of makes sense. If you have a plane with an object on it, and rotate the plane relative to a point somewhere on the plane, then the object moves along the border of the circle of a radius equal to the lenght of the distance between the center of rotation and the object in question. So the longer the distance, the longer the border, and thus the trajectory of the object becomes straighter. Thus if the center is at infinity, the distance between the center and the object is infinite, and thus the radius of the circle is infinite, which means that the trajectory is a straight line.
Simply put, as the distance between the object and the center of rotation approaches infinity, its movement trajectory during the rotation approaches a straight line.
It blew my mind when we prove it in high school but it makes sense
+j0nthegreat mind blown to infinity
+StormGaming Yes
Finally, a Numberphile video with material I can understand !!
Wow this was really interesting! I really want more of this, I wanna know why does that happen with the triangles.
i think its because the period of rotation of equilateral triangles is 60 degrees, and the square is 90 degrees.
Excellent episode, and a perfect presentation... a lot of food for thought, thanks!
This looks a lot better in real life, RUclips compresses the video (even in 1080p) which causes the patterns to not look as distinguished.
+ComputersAreRealCool It wasn't so bad at my end... But yes, since you're imposing a regular grid (cells in the sensor and pixels in the video) onto this grid yet again, the effect will suffer. Same if you scan or even re-print an image printed with offset-print, for example.
You can see the Moiré effect happening between printed dots and cells/pixels at 3:45 quite well :) That time, the undesired effect can be used to illustrate the contents of the video :D
And with compression, there are different techniques, but many divide the picture up into fields of 8x8 pixels, for example.
Incredibly fun to watch. Thank you for making this. Mr.Tokieda you're inspiring.
4:21 This explains some of the artifacts I've seen when scanning a printed document. It's a slight rotation of scanned dots with printed dots.
This may be one of the coolest things I've ever seen in my entire life.
I encountered this phenomena while working with perforated sheet metal.
Tadashi Tokieda, the only demomaker with paper, stencil and photocopier... No memory requirement, no dedicated GPU, no assembly trick... Just passion.
quite curious indeed
+StormGaming
Yes
+StormGaming Yes
Such an easy lab/demo that you can give to kids in class. I hope there's teachers out there watching this so one lucky classroom can have their minds blown as much as we did!
O-ver-lapping designs make a pattern of lines, that's a Moire!
Thats one of the more amazing vids ive seen on this channel, wow!
“This one makes You seasick”
I HAD THESE IN PRE SCHOOL. Literally one of the coolest times of my life.
I hope someone from numberphile give this man a pair of socks for christmas :D
Tadashi sir , no doubt one of the best!!
This is fascinating. I want to use this as the basis for a cyber-thriller or something. Patterns hidden in the dots!
+Take Walker Have you ever heard about stereograms?
+Take Walker Imagine being able to encrypt a complex map, hidden in an exact angle of rotation of two (or more?) layers of transparent dots.
Exactly the kind of thing I was thinking of!
Take Walker If you ever do write something on this, please show us :D
Haha, man, I have to get over my fear of writing real fiction first. XD
I love the videos with Tadashi!
I need these in the house to mess with people's minds when tripping.
This guy is awesome! I'd love to see more of his demonstrations! Those demonstrations sort of reminded me of isomeric compounds rotating polarized light clockwise (dextrorotatory) and (levorotatory) anticlockwise! That's so cool!
That's awesome. It actually answers a question I've had since I was young - why you get concentric circles when you look at a street lamp through the branches of a tree without leaves... Thanks!
When the the non random pattern showed my eyes quality dropped to 480p
I saw this (0:32) in a VSauce video a couple years ago about everywhere being the center of the universe.
+Rohan Pandey Heh, same :)
+Rohan Pandey yes they share the same idea
+Rohan Pandey How can everywhere be the center of the universe if *I* am the center of the universe?
+Extremely Sketchy You're so big that you're everywhere.
Casually says, "Translations are just rotations with center at infinity", shrugs off how mind blowing the statement was by nonchalantly moving on.
Ikr
what sorcery is this?!
+Victor Aguirre He's a sorcerer! BURN HIM!!!
My eyesssssss !!!! My brainnnnn !!! It hurts so muchhh... Awesome video :)
I'm glad I didn't meet this guy in 1970 while trippin on acid.
Why?
*-YOUR and YOU'RE are 2 different words-* your acting out again
@@thebarnyard5633 you're*
@@-yourandyoureare2different612 U and R are 2 different letters
@@sonnypruitt6639 and?
I like this guy. He gives an impression of true wisdom.
What happens if you try this with octagons or circles I wonder?
You can't really checker circles... As the intersecting point will become sides.
+Minihood31770 Yeah that's the problem (though you could certainly make patterns with them anyway) that you can't tile a plane using other regular shapes than squares, triangles and hexagons. BUT you could take weird irregular shapes and make stuff, or patterns of dots, the only problem is that you kinda need the pattern to have some manner of rotational symmetry for at least the moiré patterns to emerge :)
+Michael Nguyen "You can't really tessellate circles..." (fixed it)
---
Somebody should do Penrose.
+Alfonso J. Ramos (theraot) I apologize. You are correct.
+Minihood31770 I was testing something similar to this a few weeks ago, although I used hexagons. If you rotate the top layer to the correct angle, you can see 6 pointed stars emerge. I imagine you'd get 5 pointed stars from tesselating pentagons.
This is awesome! I love things like this cause it makes you so curious as to what is happening
Numerphile can't post on the website a kind of dots that do that to us print out?
Watching this hammered on Christmas day is the best thing EVER
I need to reset my eyes by staring at a blank wall.
Yes! We want more of this guy!
Your voice is so calming
#Nohomo
One can think of the transparency as a sampling pattern and the paper some signals. Plotting the patterns in the Frouier domain may explain the phenomenon more clearly.
Moire patterns appeared in my research on lattices in Bose-Einstein condensates, with a manuscript on the topic gone for peer review (browse playlists if you'd like to see). They are beautiful. Oh, and nice work!
0:55 After this sentence I paused the video and said "How amazing is this.".
I expected more math behind it... this felt more like was just "this looks cool, let's just show them this"
even without numbers it is still math -- this is symmetry and euclidean transformation, just not quantized. He at least points out that triangular lattices are symmetric with 120 degree rotations xD and also introduces the concept of duals, which is big in geometry and group theory.
Please do more of these videos wirh Tadashi, he's awesome!!!
I think I need to describe more things as "interestingly boring"
More Tadashi please! This guy has some genuinely fascinating things going on.
Brain.exe has stopped working... rebooting...
Tadashi san always comes with something so fun you want to show to your friends :).
MY EYES!!!!!
This channel is one of RUclips's best hidden gems (not really that hidden but you know what I mean =P )
Does +StormGaming comment No below every comment?
+TG MrNacknime Yes
Just a regular troll, I find it quite funny, sometimes. Somewhere in the world, a dude is spreading "yes" and "no" on a math channel. But you know, I'm not Dr. House, so maybe I'm a moron too, hahahaha . (Sorry for my bad english)
No
+Pedro Cavalcanti your english was fine mate, even the punctuation.
+Pedro Cavalcanti Hi. (sorry for bad english)
this guy is sooo mind blowing.. MORE MORE MORE!
OMFG he sits just like L, the bare feet and all HAHAH
+Migas Almeida Only for the first half minute though. XD And one of his legs was lying on the chair sideways under him, rather than both knees up to his chest. XD
dude, but still awesome L thingy
+Migas Almeida Ja! :P
I found that while I was playing with perfboard PCB, these are boards with array of drills. Once I placed hole above hole in both noting appeared but once I rotated one the same pattern emerged, array of circles that grow or get smaller :)