Hexaflexagons
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- čas přidán 10. 09. 2024
- Hooraaaay flexagons! Happy October. Here's part 2: • Hexaflexagons 2
Hexaflexagon Safety Guide: • Hexaflexagon Safety Guide
Support me on Patreon: / vihart
Historical Note: This video is based on a true story. Arthur H. Stone really did invent the hexaflexagon after playing with the paper strips he'd cut off his too-wide British paper, and really did start a flexagon committee (which we'll hear more about in the next video). The details and dialogue, however, are my own invention.
This video is based on, and in honor of, Martin Gardner's first Mathematical Games column from 1956, "Hexaflexagons," which can be found here: maa.org/pubs/fo...
October 21st is Martin Gardner's birthday, which is why every October the recreational mathematics community celebrates his life and work. This year we're having hexaflexagon parties. You can join in too: www.puzzles.com...
You can find more about hexaflexagons all over the internet. flexagons.net has a lot of patterns for different kinds of flexagons, or here's the wikipedia page: en.wikipedia.or...
My personal website, which you might like: vihart.com
Forget flat earth theory, I believe in hexaflexagon earth theory.
yaboiplekka cool shit DAWG
@yaboiplekka it is NOT a theory.
We live in perpetual fear of the coming of the Great Folding To The White Side
Turrebo We shall be prepared
ooh yes I believe it
Imagine having to find the area of a hexaflexagon
You could just find the area of the strip before it's folded
lilipad90 you weren’t sopposed to do dat
i mean you could just find the area of 1 triangle and multiply that-
surface area would be even trippier
Annie Widows oh god
my bed is covered in mobius strips and hexaflexagons send help
Christine Pacia no
Christine Pacia ok
Christine Pacia are you still there? Do you still need help, I mean it been three months but...
I dont know about her but I might need help. They are all over my desk...
as long as you don't have klein bottles,you are fine
I remember when this video premiered! I've had 9 years to deal with the existence of hexaflexagons and even made a few and they still make my mind melt a bit
but..you joined 8 years ago..
@@amygdal.a fun fact
You can watch CZcams videos without an account
Wild
@Slay3R_69 fun fact: you can watch videos on other people's accounts.
I'm just learning about these now and need to make one
@@dimplesthehuman6120 fun fact: you can see different videos on different platforms.
I've been trying to do this for like 3 hours straight.
I've devoted my life to this.
Oi. You found me.
This could be a beautiful relationship
Hailey Ross lol
Raven xXx me too
If this is your life, you don't have one.
I don't know why, but I envisioned Stone, Tuckerman, and Feynmann all being like 10 years old when this happened. Imagine my disappointment when I found out they were 23, 24, and 21 respectively.
+Spencer O'Dowd cheer up and imagine them in their 20s with all the enthusiasm and young wonder of 10 year olds.
Would it also interest you to know that they all went on to be great mathematicians or physicists?
They.. weren’t kids?
Argh, I was imagining it that way too!
As a 26 year old, that pleases me
Mind = Hexaflexablown
good one.
To the top!
+F Cute Hi fren |-/
Kitchen Sink hello fren |-/
+F Cute |-/
Shes going to graduate from Harvard, Stanford, and yale all at the same time
Jay Lee you kinda have the same pfp as my friend
-LLama- Well, she’s actually a teacher right now.
Huh
honeycoves wut
Oh my god I'm watching Gilmore girls and she's going to Yale and she was maybe gonna go to harvard
CONSPIRACY:
The Google drive logo is a hexaflexagon.
this changes everything
ILLUMANATI CONFIRMED
It's an irregular hexagon o-o i think
Its a mobius strip with three twists
Infinite drive space is possible
If you think about it, a hexaflexagon is a möbius strip with 3 half twists
"openupable"
There needs to be a Vi Hart dictionary.
"Snails: not stainless steel"
...
UNopenuppable, yet! love it!
Trap Music NOW. E
Y'all remember just kinda
Watching this?
Like
Stumbling upon it and just clicking on it but you can't stop watching it and you're just like
"Ah."
My sister showed me. And I was thankful from that day on
YES OMG
God I miss that feeling, nowadays I feel like we barely stumble onto things and give them any attention
i thought i was the only one wow
one of these videos got recommended to me again and now im here looking at hexaflexagons
Magician: "Sir, how many sides do you recon this strip of paper has?". Sir: "Eh? 2 sides obviously"
Magician: "Yes, but if I bent the strip like this, it has 3 sides!" Sir: "WOW!"
Magician: "And if I bend it like this, then it has... 6 sides I guess? Not really sure..."
And then he turns it into a Möbius strip to watch the world burn
@@rmeows5087 underratted reply
brb making one of these and then becoming addicted to playing with it so it breaks
TELL ME UR SECRETS
Epicalmeow TFM IDK HOW TO DO IT
ThecupcakegamerAJ ill make a vid I did it in my program
city what the fuck are you doing on Vi-Hart u are supposed to be on TFM
Help I made one of the complex hexaflexagons by spiraling the paper around and making a hexaflexagon out of that but I think I taped it wrong because there were only three sides and as I flexed it it slowly devolved into not a hexaflexagon and the colors that I colored started appearing on the same sides as other colors and there were extra flaps constantly being made. As I flexed it more and more it became even more deformed to the point where I don't think it was even a hexaflexagon anymore, but I couldn't help it, I just kept on flexing and flexing until it all unraveled and was just a weird twisty circle that was just a shadow of the hexaflexagon it once was. I decided that this needed to stop so with all my might I ripped off the tape I put on it and it turned into a regular strip of paper with a million creases making a million equilateral triangles. I honestly saw my life flash before my eyes, how could something that was so twisted and corrupt turn back into a simple strip of paper? Those equilateral triangles all staring at me asking me why I destroyed it. I started crying, why, why did it do this to me? Why did I do this to it? I couldn't believe what I had done.
Red5rainbow
Deep.
one like equeles one prayer
One like equals one spelling lesson for this poor soul
I hear they have pills for that.
Crippling depression 101
I made a hexaflexagon out of a fruit by the foot
Maddox Boykin that is so lit
Maddox Boykin, THAT'S cool
*WAHT!!*
Lit
wait..how did it not stick? ohhhh did u not peel it?
11 year old me was not ready for the mathematical, life changing beauty of the hexaflexagon. Still finding this video all these years later. Time to make another one or two or dozen or hundred
Mathemagical ❤ Be sure to watch Vi's "Hexaflexaflakes" vid
had to watch this at school 5 years ago. just found this channel by accident .
Same!
Emas
lol my math teacher told us to watch this
sames
Ours made us watch *all* of ViHart's Hexaflexagon videos.
In class! So that's cool.
xD
Kathy P This is Best Math Resource Channel EVER.
your math teacher is amazing
I have homework to do and I'm here learning about the art of hexaflexagation
Who else is getting this recommended in 2019?
I am and I’m happy
Aye me
Yeas this is FUN
Me but it’s pretty entertaining
Me but it's cool
And now I will never be content with myself until I figure out how to make this. No tutorials help lol. XD
+EMan753 same, if you find one can you link it?
+EMan753 at the end it kinda gives one
+EMan753
Bump in case any of you found one.
i have made 2 myself, but the last step is kinda like bend it untill you figure it out XD
blazic I still have no idea how to make it :'(
I need a tutorial I can't make a hexaflexagon
Yea same I tried like 1000 times and I just failed :;
start with an angle of 60 degrees. If you start folding you should notice that now all sides of the triangle have the same size.
Same!
+SkyWolfGaming365 well i made a tri-hexaflexagon and a hexaplexagon/complhexagon... Its Complex i guess
Get a thing piece of paper, around 7 cm. fold a 60 degree triangle and then fold it over to make a full triangle. Continue to fold it accordion style until you have 9 triangles. Cut off the excess tris. Go to the third tri and fold it left...... Hold up I can't explain this just watch a vid
WHY IS THIS SEVEN YEARS OLD IM SO SAD OML
Because it was released 7 years ago duh
It’s Time Maddie
My math teacher showed my class this when I was a sophomore. I remember her being so excited to show us it, but she just got blank looks from the group of 15 and 16 year olds who could not comprehend the hexaflexagon😂
You've ruined my life. This is all I can do.
Change your name to: Hexaflexagon Addict.
Improved*
I just realised a flexagon is a mobius strip folded uo into a hexagon...wau
Wau!
hi @Michael Darrow
*finished video*
Me: "MUUUUUM, WHERES THE PAPERR?!?!"
Mum: why do u want it sweetie?
Me: "I NEED TO MAKE A TRIHEXAFLEXAGON!!"
Mum: uhh... Okay, dear...
Lol
xD
*MUUUUUM*
Deer**
Богдан Семенов ***dear
That's why, hexagons are the bestagons. And the proof, are the hexaflexagons.
If I ever had to hide information, I'd put it in a hexaflexagon
"Openupable"..
I'm expanding my vocabulary hence forth...
“but bryan doesn’t have tape, after all it was only invented 10 years ago” kadnenieisid ok BRYAN
this is a comment going down in history
You would not believe how many minds of Number Theory students at CTY you blew with this video. Been a fan since it was still like only a year old, excited to have found it again!
So that's where EXO got their logo...
Omg yes
Sksksk-ahgsnajhs 😂😂😂
that’s what i clicked on the video for lmaooo
I for real though it was exo logo
That’s why I watched the video!
i just spent an hour trying to find a side on my newly created trihexaflexagon. so proud i finally got it. thanks so so much, this is all such a huge inspiration!
what the fuck did i just watch...
+Dounutlover 299 here....
Have An Official CZcams Nobel Comment Prize.🎊
You just watched hexaflexagons
A hexafelaxamess
#Hexafelaxamess
Hexaflexaception.
9 years, and within the past 3 years I have been obsessed with making this out of different materials and sizes. Really, thank you for introducing this amazing thing hahaha
I'm sorry but what did I just watch and why do I love it?
I can’t believe it’s been a full decade since this video!! Just made a hexaflexafon today and remembered how much I loved this 10 years ago, when I was like 11!
I introduced this to my class, and they all got so sick of it because I talked about hexaflexagons everyday haha lol WORTH IT
One of my FAVORITE videos from the good ol days 😭 I will NEVER forget the hexaflexagon
That is such a throwback. It was just in my recommended and I can never not watch hexaflexagons.
Flashback?
OMG. how am i discovering this only in 2019. my childhood could have been so much better.
2:43 what went through my mind during Steven Universe: change your mind
||-//💛🖤
nice
10 years later, still a comfort video, thanks Vihart to be so openly "you"
It's nice to see people as particular as self when you feel off. It allows self to say "hey ok, I'm a bit awkward, but that's fine and kind of cool"
Me trying to sleep at 1am:
Hexafelxagons: not today
Tomorrow
Tomorrow
Omygod
Tomorrow
Tomorrow
Tomorrow
HEXAFLEXGON DAY
TOMORROW
YESSSSSS AND THIS WAS 21 HOURS AFTER. THE ORIGINAL COMMENT
+Read The Description! SUNDAY SUNDAY SUNDAY BE THERE!!!1! OR BE SQUARE, OR WAS IT BE THERE AND BE HEXAFELEXAZAGONAL! I THINK!!1!
Why, in the 9 years this has been on CZcams, was I not recommended this
My friend tried to being these to my school, never got anywhere.
Now I need my own hexaflexagon.
Omg I can't believe this was 10 entire years ago, .. I still watch vihart ALOT today, and enjoyed the hexaflexagon series alot
One of my elementary school teachers showed us this exact video many years ago, likely when it was new. I never forgot how to make them. It was nice to see this in my recommended.
After watching this for the forerverth time I made a flexagon, one for each of my members of my family, and much more. I have spiraled into hexaflexinsanity.
Also I think I'm set for every car ride.
Hexaflexa life bb! ✌
I'm actually sitting alone in my room spending hours at a time trying to figure out how to make these but crying because I can't. WHAT DID YOU FOLD TELL ME THE SECRETS
Did you find out
@@Mewtic1 TELL ME IF YOU HAVE BECAUSE I NEED IT
@@toast_toast1206 there are tutorials online
ik you commented this 6 years ago but ik how to make it so if you need the info just reply
I find this video very intriguing because the flexigation complexity relates to the mathematics of knots. The lattice of the design would keep showing more and more sides even when you didn't expect them to come up. A confusing part is why more than 3 sides that needed to be colored showed up after only the first time there were 3 sides. I've heard of origami and I would like to know more about the intricate balances in lattices that appear to want to come apart, but it's almost like a mysterious, mathematical, universal law of matter that keeps everything together. It's inspired me to keep trying in life, and even when some doors close, some doors will open anew. And doing the right thing will lead to positive results even if things look bleak.
I just found your channel again after maybe a decade. And I've realized that so much of how I see math is based on the inspiration you gave me years ago, and I hadn't even realized it. You defined a passion of mine at a crucial moment and I sincerely thank you for that.
Not to put pressure on you, like it's your duty to do that. But you happened to enlighten me and likely many others, and deserve credit.
i come back to this video every once in a while because it just interests me so thoroughly
No one
CZcams 2019 : alow us to introduce myself
JustAburrito yeet allow US to introduce MYSELF
somethings wrong right there
My grandfather showed me one of these when i was younger and how to make one but I could never duplicate it later and didn’t know what they were called. He passed several years ago and this reminded me of him. I’ll have to make one later.
Did you make one? Hoping!
Holy shit I've never been so interested in shit like this
my 9th grade geometry teacher showed us this video along with some of your others when we had extra time before the bell and here I am 8 years later seeing this in my recommended and wow the flashbacks I got. I used to make these ALL the time after he showed us this video. time to watch everything else you have and reminisce
I remember watching this in 6th grade for "Fun Friday"
I remember watching this a few years ago so many memories
When the invented 10 years ago line still applies:
i love how this is explaining how u make and use hexaflexagons and what they're all about but also explains how they were found
The word trippy doesn't explain how trippy this is
Gay ™ ...
Gay ™ hello gay. just saying hello. have a gay day. your gay friend
Holy hell. I remember this video from long ago. I kept making these and flexing it, helps when I'm nervous, gosh. How the time flies.
I remember I was just watching this channel two years ago and now you have almost a million subscribers!
I love your username
AmazingPhilIsNotOnFirePanicsAtTheDisco holy shit the emo trinity and phan are fucking everywhere and I love it xxx
after three mere tries, i have mastered the art of...
HEXAELEXAGONS!
HOW??!!
oh my god. I saw this video 8 years ago, and fell in love with this channel, but at the time, I didn’t have a youtube account. Around 3 years ago, I remembered the channel slightly, but just could not figure it out. ever since then, I’ve wondered if I would ever find it again. until now, when a video about spongebob’s house design changing showed how YOU helped change it. I’m so happy I found this again, time to go watch candy button mobius strips and logarithms.
STOP STALKING ME!
sorry
LOL
Btw you are almost out of milk
what do u mean?
🎶what do you mean?🎶
the fact that hexaflexagons exist is amazing
“Where did the yellow side go?”
Symmetry: Am I a joke to you?
This was the start of my origami journey
This has been made more than a decade ago and the hexaflexagons still linger in my mind.
Why did I just discover this channel in 2019??
I took a graph theory class from Arthur Stone in 1968 (and a topology class from his wife in 1967).
HELP MEEHHHH I CANT FOLD EQULATIRAL TRIANGLES!!!
Lol I had the same problem 😂
You can just measure the angle. For Equlatiral triangles its 60
+Katherine Yan my Equilateral triangles have 90 degrees each angle!?
OMG i had that same problem! my paper looks like sqares
i made one that does not flex and has only 2 sides.
when did willow from buffy start making hexaflexagons?
I think she sounds like Felicia Day
Aaron flexes in!
*you flex harder* *Aaron flexs himself even harder* *Aaron flexes himself out of the room*
+banana derpington holy shit I've found my people
Elliott Belardo
i just subbed to you
Duh duh da duh
I was completely blown away by this hexaflexagon video! This little origami piece was really inspiring to watch because of all the sides the paper could have by simply folding a little piece of paper. The complex patterns and the way they changed with each fold fascinated me. It's incredible to consider how something as basic as folding paper can result in such interesting and intricate geometric designs. Watching this video has sparked my curiosity to learn more about the mathematics behind hexaflexagons and perhaps even try making one myself. Overall, a captivating and educational watch!
I just realised that a hexaflexagon is like a Möbius strip with 3 twists in it (more for the hexahexaflexagon of course).
Its a digital möbius strip! :O
I thoroughly enjoy your strange one yellow sleeve, one black sleeve attire. Go you mind-boggling math-magician, magic mathematician.
Wait, wait, wait... I just had a great idea we could use Hexaflexagons as like trading cards :O all you have to do is make a list of rare colours and what type of hexagon it is and then if it's a Rae colour you trade it with someone who has a good "card"
Have any suggestions or different ideas?
l forgot about this channel for a while but decided to check it out again when l randomly remembered hexaflexagons. its been so long that hearing this story now is as enteraining as when l first heard it :)
*cries while holding a crumpled strip of paper*
Therapist: Hexaflexagon can't hurt you
Hexaflexagon:
We made these in math and everyone was playing with them at assembly instead of paying attention. It was so funny.
This is a really old video. I'm glad I bumped into it. Now I'm gonna make a Hexaflexagon.
Holy hell we'd be best friends in 4th grade.
You blew my mind.
Ayeeee Napsta!
+Gracelynn Reneau I am actually a hacker.
o-o
+Gracelynn Reneau (but not really)
+Gracelynn Reneau Or am I?
1:17
*”OPENUPABLE”*
OMFG.... I love this channel. Just stumbled across it and this was the second video and now I have to binge watch all of them... but thats epic!
I wish I had this much fun in school.
found this a year ago, fell in love, decided to show it to my friend in class, he fell in love
Cakie Boi w i t h y o u?
@@k8tieisjusthere123 mission succsessful ngl then
This is by far one of the coolest shape/paper object that I have ever seen in my life. The way that it is able to turn and turn coming up with surprises every once and a while with a new white side, not only amuses me, but confuses me at the same time. One thing that I don't understand is that when you were doing the hexaflexagon with more than three colored sides, why were you getting the same three colors in a row multiple times and then out of the blue you will see another random white side? I would figure that all the different sides would come one after the other instead of repeating the same three and them having another white side come out of nowhere.
I've used this in my 4th & 5th grade class. Just to see the joy in their faces that math can be fun is worth it.
what am I doing with my life...
|-/
using it wisely
Hello, fam |-/
Great things
good things
I'm just now watching this in 2019.
CZcams, dude.
2015:No
2016: Nada
2017: Nein
2018: Niet
2019: random ass video about a hexaflexagon
The way of tellng the story has a very hypnotic effect, giving me a catatonic look on my face and brings back memories of being 15 and being bored in class very vividly... excellent job..