Tessellation Is Easier Than You Think
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- Опубликовано: 8 ноя 2021
- I show you how easy it is to tessellate
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That’s really interesting James. I always thought tessilation required super specific shapes
Nice to see you here I love your videos
Love your channel and also tetrix
I just realised i didnt know his name
Again same recommendation
please tesselate plasma
In high school art class we learned to create tesselated shapes by cutting into a square and taping whatever you cut to the other side. It works horizontally and vertically so you can get some surprisingly complex results with a few cuts.
"You can't tessellate pentagons."
*Flashback to penrose tiling*
Marjory is impressive. I sent this video to my wife actually before I saw that part because our two year old just got a new toy that is geometric shapes that magnetically stick together and I can tell that they really did their research in choosing the shapes because I love using it to teach my son two and three dimensional geometry and have made some pretty cool discoveries playing with them.
Hands on manipulatives are a good way to learn!
Sounds like you're having more fun with your son's toys than he is lol
Please, what is the name of the toy?
What were your parents thinking when they named you? 🤨
@@swear.157 Not my name but if it was that's about exactly what I'd ask if I were you lol.
The story about the pentagons is amazing
random stay at home mom creating complex geometric solutions for fun
ANY hexagon whose opposite sides are parallel will tessellate. You pretty much demonstrate this using your 4-sided figures. There are plenty of non-convex hexagons which will tessellate. There are only 3 *irregular* convex hexagons which will tessellate.
Or maybe honeybees are impossible!
Glad I'm not the only one making this point, although I'll add there's a great deal more than "plenty" of non-convex hexagons that will tessellate... there's infinite.
@@ongbonga9025 Do you know if there exist any non-convex hexagons which have *aperiodic* tiling rather than periodic tessellation? (I'm just too lazy/busy to try and look that up right now)
Perhaps the greatest at this was M C Escher, he made tessilations that transformed into further tessilations of different shapes such as birds
Birds are, by definition, quadrilateral. They always tesselate.
@@Blahnik1182 lol
I have a large print of 'Sky and Water ll' it's like a tessellation, but I think it's referred to as 'division of a plane'
@@Blahnik1182 Is this a joke? I don’t know if it is or not.
@@Blahnik1182 Most of them also migrate, except for like chickens and emus and stuff.
Thanks - you took me back 54 years to my 7th grade geometry class! I really appreciated that.
You and your channel never fail to inspire me.😊 Appreciate, thank you
What I find fascinating is how soccer balls are made from a combination of both pentagons and hexagons, all of which are symmetrical.
Just curious if anyone else had the first reaction of not cutting the paper at all and leaving it as a rectangle? :)
I knew there had to be more to it than that, but yes that was my first thought
Haha not me, but I can totally see it now.😅
I was like, "oh no, I guess that's technically not a square but I feel robbed nonetheless" lol
Well he did say to cut one out so, yes, cut straight across to make two rectangles.
Cut a square.
*These complex tessellations is still easier to fitting than me trying to fit myself in the group of friends.*
deep
How to create tessellations with more sides: Take a rectangle and cut out anything from one side and the adjacent side. Then tape both pieces to their opposite sides. This shape will tessellate a plane.
This is awesome❣ Thanks for sharing.
Seriously James, your channel is in my top 5. Thank you!
Thank you so much for going a bit more into the mathematics behind tessellations... this is basically the only thing I remember doing in high-school trigonometry, it's nice to be reminded of the "why" behind the mathgic.
4:35 Incorrectly said. You can have more than 7 sides and tesselate if you use interior angles.
For example FℲ makes a rectangle and each F has 10 sides and rectangles pave the 2D space.
He ought to have specified ‘convex shapes’.
Nice job, James!!
I discovered an octagon that tessellate.
Try it with a thick lettered 'E' without this '-' inner line in it
its an irregular shape, there are infinite irregular tasselation shapes
he s talking about semi regulat
No wonder a mom added to it. The picture with this definition was a QUILT! "A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries." And of course a quilt serves a PURPOSE. It is using up scraps of fabric after it has been used to make clothes. So its secondary purpose is to form memories. Often the family can gather around the quilt, point to swatches and say, "hey I remember that dress, shirt, skirt, pair of pants, etc." As they keep warm under it.
I owe this guy so much!
OMG! When he started I thought this topic was stupid but i kept watching and now it's my favorite action lab vids ever. I got it. I was so stimulated. Wow! 360. I'm forwarding this to my quilter friend now.
Thats awesome, I like that Marjorie Rice discovered something on her kitchen table that mathematicians missed.
The only man to make simple geometry the dopest shit on RUclips!
I guess that explains why a circle cannot tesselate. It has infinite sides!
Circles have ZERO sides, friend. I mean, it's IN the shape itself--a circle IS a zero.
@@michaelmccoy1794 ah, my friend. There, you could be wrong! A circle can have zero, one, two, or infinite sides.
Zero: a side could refer to a straight line
One: one curved line, going around in a circuit
Two: inside and outside
Infinite: lots of tiny straight sides
ruclips.net/video/sfilRCCtJtA/видео.html
This is the first time I really get what tessellation is, what a great video! thanks!
Wow! This is crazy interesting, all of your videos are!
I saw this in the 90s on the Curiosity show. Amazing to see everytime.
Me as a origami artist I love tessellation
In 3D graphics we use the word tesselation to describe how polygons are broken up into triangles.
Now I want to go program a program that finds all the missing tesselations :)
This is very interesting knowledge. Thank you for the amazing video. I will do my kitchen floor using one of the pentagonal tiles.
A great video, like always. But a question, I think you were upset or not as energetic as always on the recording day. Hope everything is going well and smooth for you and your family. God bless you bro.
Thanks James I've learnt a lot and for real I don't know why someone could dislike this video...but well it may be their preferences..not judging
Cats playing with mouse?
Judge away. Your allowed to have an opinion.
I remember watching a numberphile video about regular polyhedron in higher dimensions
You sir are an outstanding presenter. Thanks
This is really useful while making mechanical parts . Good work 👍
Thank you so much, I never really understood what this term meant until now, have seen it as part graphic settings in video games
Let’s go another upload
I was certain you would mention Penrose tiling somewhere in the video.
Love this video. I have been fascinated by tessellations since I was a child. In a larger repeated tessellated pattern what is the lowest number of colors needed such that no two shapes of the same color touch?
Related to cartography.
Do corners count, or just shared sides? Asking for Utah Colorado Arizona and New Mexico
Do corners count, or just shared sides? Asking for Germany France Poland and Sweden
Do corners count, or just shared sides? Asking for Austria Ireland England and Iceland
3 or 4, depending on the tesselation.
This is super interesting!!!
i am 13 years old and i have been learning this for 2 years (one month each grade)
so i am pretty good at this
Tesselation has always been my favorite kind of visual art, and I feel blessed that you made it interesting.
Could you be a fan of M C Escher's?
thank you fore this video
I loved the history in here
Hello Sir, You are doing a great work
Thank you very much
Love from India
😊😊😊😊😊❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
So I literally drew tessellations for years starting in High School during boring lectures. I have notebooks full of tessellations using different shapes. I never knew this is what a repeating pattern such as this was called though!
Thaaaaanksss!!! ✨😀😀😀
Huge fan! Can you cover the chaos pendulum one day?
Your result about shapes with more sides must have specific rules because you can use a quadrilateral as a base shape and then make one of the sides jagged so that it still fits with itself when you rotate it 180° this can have any arbitrary number of sides and will tessellate the plane.
That type of mom is really strong
Bro legit saved ❤ my life
Can create beautiful geometrical shapes with this technique.
Me watching this on the toilet with the volume all the way up. My Dad in his bathroom hearing, "Today I'm gonna teach you how to tesalate." 😳
Off to build a tesselation tiled floor will look great
We had to make tesselations in my 6th grade class! It had to be asymmetrical and contain at least 5 sides too. It was a lot of fun trying to figure it out. Mine ended up as a turtle made out of hexagons.
i will probably notice this during the next visit to Floor & Decor
Holy moly, that mom rocks !
That is fascinating.
You are incredibly good
alt-J "Tesselate"
The perfect soundtrack for these kind of topics and inquiries. 😊
Who remembers when his channel was small and he was just a guy crushing things in his backyard
Great video, like other users i just to think that was a really hard job to find shapes that can fit in pattern
The stay at home mom: hold my baby i need to proof this mathematician wrong!
Amazing Information
Great
I assume you would say mc escher tessalations are built from square or triangular bases actually ends up being interesting that it works around the square or triangle limit.
Great videos .......
Love from INDIA❤❤❤
Wow Awesome!
Dear Action Lab:
I have an experiment Idea:
Explanation:
a tiny glowing orb which hydrodynamically resembles a floating star, complete with sunspots and coronal ejections.
Forward:
I know I am not a patreon supporter, but please consider trying this suggestion anyways, or perhaps suggest it to them.
This morning I conceived of how to make a dynamic model of the sun, in a jar.
It was complicated.
I will not bore you with the details.
A simpler similar experiment you could do on the cheap would be this:
Set-up:
Some autozone uv oil soluble luminescent dye, mixed into ferrofluid (it's oil-based right?)
Cold LN2 temp super magnet.
Magnetic coil used for heating cold soldering pins through magneto constriction.
An airtight container
Tape; a drill bit & caulk.
Measure the average height range of the floating glob of ferrofluid as seen in the set up from your past video;
Place a container over it, tape the magnetoconstrictor center level with the average of the range.
Drill and caulk a hole for the power plug.
Then perhaps make a drain/flood plane you can fill with LN2, or not, it can also be a flat piece of plastic.
Put the chilled magnet and floating ferro fluid in place, so that they mate to the center of the magnetoconstrictor.
Also, prior to this, mix the glowing dye into the ferrofluid sample.
Quickly caulk the bottom of the container so that fumes don't leak.
Turn on an overhead blacklight, turn off the lights, plug in the magnetoconstrictor to power.
Boil some zero-G glowing ferrofluid in the dark, and be amazed if you can.
I suspect this would resemble a miniature sun, although it might just create an oil fire. So take the necessary precautions.
Perhaps fill the container with that coolant that behaves like water but is in fact a chemically inert gas? (Sold by 3M as Novec for flame retardant electronic coolant I believe) (only do this if it is safe I do not know if it is safe yet that is why I am asking the pros like you to weigh in)
In which case you may have to drill two additional holes and install valves, for letting air out while you fill the chamber with something non-flammable.
I believe this could be of benefit to experimental stellar dynamics so please try this.
I also think it would be the mother of all desk ornaments.
I will also forward this letter to Cody's Lab and to TKOR, because I like them equally and they also further free science education just like you.
I love all you guys thank you for reading this, please be safe, and I am okay if you reject my idea.
I am better than okay if you accept my idea, however.
I am excitedly awaiting a response.
I am a dork.
Thank you -all.
-Sincerely Nia.
To harness energy from it, or to deal with expansion stress, I imagine: tying a balloon to the output nozzle would work.
Utilizing the design meant to be filled with novec ofcourse (the one with two novels on the top)
I also think a hydrostatic system of LN2 with u bend gas trap like a toilet, and the magnet in the reservoir, or a cheaper system with a T wall and a gap at the bottom, would be best for keeping the magnet cold.
The ferrofluid will get hot, so it will need to be in am inflammable substance.
So the final design would be a triode for fluids.
1st stage: place magnet in tray and fill tray with LN2.
2nd stage: place ferro fluid glob into magnetic locking with magnet.
3rd stage: place modified container dome complete with carefully placed alternating current magnetoconstriction coil over magnet.
4th stage: seal air tight. (It's air tight so long as the LN2 reservoir is full).
5th stage: replace air with Novec or Argon or similar fluid substance*
*note: novec might displace LN2, so Argon may be Argon, or Nitrogen gas or a sealed reservoir may be superior.
6th state: place deflated balloon onto output nozzel.
7th stage: power on.
Once the ferrofluid begins to boil, I predict the air in the chamber will want to expand, so if the balloon starts to inflate, it may be wise to turn off the power at a certain size of inflation, and allow the system to cool.
If you have a power control timer, or a light switch and good rythm: pulse width modulation based off of the inflation of the balloon, might be required.
Ie: turn it off and on again, and again, and again, to keep the balloon from popping.
Just a last minute concern and hot fix idea I had.
This harnesses, energy, since the balloon could be replaced with a gas piston.
I doubt it's an efficient energy source, but if thermal expansion proves to be an issue then it's technically an engine of some kind albeit probably a horrible one.
It's mainly meant to be a pretty floating thing that shoots off globs which get pulled back in like a star, and glows and has chaotic ccurrent.
I don't know if it would work, can't build it myself because of my living conditions.
Umm... yeah.
The balloon fix.
There ya go
Or put it in a really thick pressure chamber which clamps down into place so that it doesn't explode when it expands outwards, and then cool an external magnet with whatever works since it's external and doesn't matter as much, and then the only thing on the inside would by the constrictor.
I'm lost in thought. I wonder if aquarium glue would be strong enough or if stuff would leak where the power cord leaves.
Like I said, an ambient pressure system with a balloon and someone with safety glasses earplugs and a fire extinguisher and a light switch controlling the magnetoconstrictor, might be the cheapest reliable method, but I'm kind of inexperienced, so........... (trails off)
Do you're best yo✨👍
Perhaps a steal plate with the magnet on the outside in a bucket of ln2 could be an improvement to this design, since the field would permeate in, right?
If it's supercooled it might need to be duct-taped to the steel plate so the steal doesn't levitate around, right?
I don’t know, just a last minute suggestion, because I'm excited and thinking about this a lot. Sorry
If you replace the mag lev, with sono lev, the number of power cords goes up, but, it theoretically lasts indefinitely (instead of needing a constant renewal of LN2), so there you go, I guess
For Pentagons, you can probably derive some kind of rule that breaks it down into a quadrilateral and a triangle, that must have some certain range of relationships, angle-wise.
This is the nerdiest thing I have ever seen. I love it!
What is so wrong with us is that whenever we told anything we just believe it blindly without thinking about that it could be wrong ir if it is right then is it possible that this can also be right.
Cooooool!!!
James, I always got the feeling you were a member of the church of Jesus Christ of Latter Day Saints. I am too! That’s so cool! Your light and passion for science really does shine! Keep up the great work and positive vibes you bring to your channel! 💓
Is he though?
@@Majin_Sophax I thought so. I looked it up on google. I could be wrong obviously, but it seems he is :)
Fractals and Madelbrot set interesting also.
Sir I have a doubt in your past video you made an expriment in that freeze the water it expanse and blast the container . So will water really contract are expand during freezing
I remember doing this back in 3rd grade
Nice shirt!
Good Job.
A few small corrections and remarks:
The 15 convex pentagons that tessellate are really 15 families of pentagons. The members in a family can all tessellate in exactly the same way, they just have slightly different dimensions. The same is true of the 3 families of tessellating hexagons - the regular hexagon actually fits into all three of those families.
In 2017 Michaël Rao proved that the 15 convex pentagon families are the only ones. Although his proof involved computer searches, it is generally accepted as correct.
There are shapes with 7 or more sides can tessellate provided they are non-convex. Convex heptagons/octagons etc can never tessellate. An easy handwavy proof: Convex polygons have vertex angles less than 180. So at every vertex in the tiling there will be at least 3 tiles meeting. Therefore the average size of the vertex angles of the tiles is no more than 360/3=120 degrees. Heptagons/Octagons etc have a larger average vertex angle and so cannot tessellate when convex.
If you want to see more about pentagon tilings in particular, I did a 5 minute talk about them:
ruclips.net/video/MK5dyGjLOnA/видео.html
a seven sided shape would tessellate if it were a rectangle with two equilateral triangles on one side creating one shape, a nine sided shape would too with three triangles on one side, in fact any odd number of sides can use that pattern. You could also make the opposite side a triangle instead of a flat side and do any number of sides since that makes an even number and they'll tessellate with a zig zig on one side and a different zigzag on the opposite side as long as the opposite corners have the same y coordinate. You also should be able to do any number of sides by taking combinations of a set that already tessellates into a finite pattern and just calling the repeating group of shapes one shape.
I wonder if you can scale the size of the shapes however you want does that change how many shapes can be tessellated?
Hi, does anyone know what platform / medium available like in 1:04 that allows you to create shapes and experiment if it tessellates?
>Sees things neat and orderly
>*Happy brain noises/chemicals*
You know that vidio you posted 3 years ago? The one with the electric motor? Do you still have the motor? You can do a race with a drone.
😊
What is the temperature at the point of contact when an object of temperature -50C and an object of 50C touch at an ambient temperature of 20C ?
Dear James, your apparent "one single shape" example famously contains, as I'm sure you know, _two_ carefully constructed rhombus shapes, which together can tile the plane aperiodically. By the way, have you (or has anybody reading this) ever heard of Penrose ducks? I have a vague memory of a single, vaguely duck-like tile that could fill the plane without forming a regular pattern, but I can't find any reference to it online.
Some Cowboy: "Texagons" **cracks whip**
Tessellation … I learnt something new! 😏👍✨
Where were you during my highschool geometry project :/
Sir can you please tell me which software or application you used for the simulation ? If any other knows it please tell please.
That's really cool
Hi James, I’m assuming that these excellent presentations are targeted at kids and teenagers. I’m 54 and I still enjoy them lol. Thank you for your efforts mate. Greetings from Australia 🇦🇺
Inmean, considering the fancy words he randomly throws in, they’re for anyone willing to watch them
QUESTION??
at 2:55 would the newly created shape on bottom have a combined valuel of 360°
No, because it is a pentagon. Pentagons have a sum of all interior angles equal to 540°
uncle can you put a video on infrared light
You said that nothing with 7 or more sides will tessellate. I assume you meant no convex polygon with 7 or more sides, right? It is pretty trivial to make a concave octagon that will.
I would assume so.
My 8th grade math teacher had the whole grade make tessellations. My design had a hundred something sides (can't remember the exact number now, but mine had the most sides by a large amount), and I colored them to look like 8-bit video game Godzilla like creatures. It was definitely a concave polygon, they're literally child's play.
The standard hexagon can also tesselate like a beehive. You didnt include that.
I KNOW RIGHT FINALLY SOMEONE WHO NOTICED, HE DIDNT INCLUDE THAT AT ALL.
EXACTLY
Is this related to fractal patterns at all?
*✊✊💪The adventure of life is to learn. The purpose of life is to grow. The nature of life is to change*✊💪💪
All about that sigma mindset
Too bad I can't do any of those, as I will probably die soon
@@TheRatLiker No no no. Why?
Gotta love sir Roger Penrose