Hexaflexagons
ฝัง
- เผยแพร่เมื่อ 30 ก.ย. 2012
- 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/focus/Gardner_Hex...
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/hexaflexagon/
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.org/wiki/Flexagon
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
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 TH-cam 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.
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
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 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!
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
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!
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!
One of my FAVORITE videos from the good ol days 😭 I will NEVER forget the hexaflexagon
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"
That is such a throwback. It was just in my recommended and I can never not watch hexaflexagons.
Flashback?
That's why, hexagons are the bestagons. And the proof, are the hexaflexagons.
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.
Omg I can't believe this was 10 entire years ago, .. I still watch vihart ALOT today, and enjoyed the hexaflexagon series alot
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! ✌
Why, in the 9 years this has been on TH-cam, was I not recommended 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
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.
i come back to this video every once in a while because it just interests me so thoroughly
the fact that hexaflexagons exist is amazing
This was the start of my origami journey
When the invented 10 years ago line still applies:
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.
This has been made more than a decade ago and the hexaflexagons still linger in my mind.
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 thoroughly enjoy your strange one yellow sleeve, one black sleeve attire. Go you mind-boggling math-magician, magic mathematician.
I took a graph theory class from Arthur Stone in 1968 (and a topology class from his wife in 1967).
I remember watching this forever ago and loving it. Vi is forever my favorite video maker, they’re so cool
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 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!
This video left me entertained the entire time. I enjoyed the story telling element and how the content of the video was presented. Between the different ways they fold, all the sides, and the different faced hexaflexagons I really enjoyed the video. The different sides of the hexaflexagons just kept multiplying!
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 :)
This is so cool! I have a lot of videos to catch up now that I have discovered your channel!
I think I’ve just discovered the most adorable voice ever. I can’t describe how much I love the way you talk and how your voice sounds. So cute!!!
This video randomly came up for me many years ago. I'd always hated math but Vi got me curious. Weirdly, I understood this! Few years later, I was diagnosed with autism and dyscalculia. My world blossomed.
Turns out, math teachers who insist students must "show their work" or fail, are the problem. They assume we cheat when we get it right. Vi explains so well the thought processes of real mathematicians! Seeing it literally unfold 3d in front of my eyes, it finally makes sense because that's how my head solves math problems. Flappy flaps and all 😅
I am SO happy to hear some math teachers now show Vi Hart videos in class! 🎉❤ I raised my kid with Vi's videos, she couldn't show her work either but I fought for her correct answers to be weighed correctly.Hexaflexin' 4 life ❤
After watching this, it became my favourite childhood toy. Im so glad i found this again in my late teens ♥︎
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.
I just taught my lil sisters how to make hexaflexagons! They really enjoyed making and flexing them, and I’m sure that they’ll have lots of fun with them in the future!
Kuhweshion: Could you say the act of folding it within itself is an act of going a higher dimension like space folding? I don't know I saw a three-sude isometric cube when you started coloring and then thought about the tesseract animation that illustrates the 4th dimension... Connecting random dots. Cool video.
This video changed my life when it came out
This video coming in my recommendations unlocked some old memories
It’s sad how she says that will have to wait until next time, but that never came…
Nvm, I didn’t realize
0:22 I was literally just making a paper spring then you make one
My high school geometry teacher, Saul Schachter, introduced us to hexaflexagons back in 1970. Great fun!
real magic
Holy crap my math teacher showed us this like 6 years ago and I just found it again
I don’t know why this is getting recommended to me after 9 years, but it’s so interesting revisiting this. I remember where I was when I saw this for the first time all those years ago
“Where did the yellow side go?”
Symmetry: Am I a joke to you?
I often find myself coming back to this video.
I feel like I just had a stroke watchin this, guess I’ll be awake tonight thinking about hexaflexagones
our teacher played this in class and we all made hexaflexagons and that is a core memory
Why is this so cute I'm confused
this video is the give me nostalgia, and so do flexagons
I love how she writes "hexaflaxagon" offcenter on the paper because the guy was used to the English papers witch are wider
9years of keeping me mentally stable. Good job Hexaflexagons!!!
wow this brings back memories
i have come back to this, and i’m still more interested than actual schoolwork
I'm working on trying to make a hexahexahexaflexagon. 37 triangles.
1 Day Later
UPDATE:
I've done it! I've made the 12-sided hexahexahexaflexagon! I have the "code" of numbers in a safe, I will share it with anyone who wants it!
Do share.
@@lagrangepoint9386 I'm so sorry, but I lost it a couple months ago :'( I am working on remaking it right now, but it'll take time
Edit:
Side 1: G124431552366124431552366124431552366G I think
this was boxxy but for math nerds
This is actually very cool, I didn’t expect paper to get me this intrigued into geometry 😄
So the 6 face one would be the sexahexaflexagon
This is awesone
First off, this is a really cool concept, and it's really confusing at first. It almost seems like an optical illusion, but the actual hexaflexagon is strikingly real once you make one for yourself, and actually fold it into itself, it's a really weird feeling. It doesn't feel real at first, and then you immediately understand the thing itself is actually quite simple. I've always been quite interested in geometry, and little cool tricks like this are so fun to learn about!
oh my god i remember being so obsessed with this video when i was a kid
NEW MEMORY UNLOCKED, NOSTALGIA HIT
Your videos are very well done and very informative. You are super intelligent. Keep making videos please
oh no here i go down another rabbit hole of stuff that's fun to look at for no apparent reason and is also like 10 years old
Just came back here to thank you, I've been subscribed to you for a long while but I have to tell you this story, years ago when I was still a kid I stumbled upon this video because I loved watching your content and as soon as I finished watching it I had asked my dad, *I need paper and scissors right now,* needless to say I developed an obsession which caused me to want to make flexagons every single second of the day, in the middle of class I would make an abhorrent amount of them, pocketsfull, decorate them all with makers, I'd decorate them with doodles, my favourite song lyrics, or even puzzles/runes I made up, it got to the point where I had used up my entire fifth grade class' worth of paper for a whole year, in half a year, and when my classmates asked me why *I solely* had used up all the paper for the class, I told them about hexaflexagons, obviously curious, they asked me what they where, which resulted in me teaching my whole fifth grade class how to make them, and some girls quickly learned and soon started to make their own. It's been a long time since that happened and I don't keep in touch with any of those kids anymore but I'd like to thank you, extremely, for creating my class obsession and frankly innert distraction for that whole school year.
Oh my gosh I watched this in AELP a while ago and got so excited when I saw this I'm crying lol
i finally found your channel again after 6 years😭
Mind = Hexaflexablown
good one.
To the top!
+F Cute Hi fren |-/
Kitchen Sink hello fren |-/
+F Cute |-/
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'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.
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
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
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
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
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
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
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
I have homework to do and I'm here learning about the art of hexaflexagation
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?
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
"Openupable"..
I'm expanding my vocabulary hence forth...
WHY IS THIS SEVEN YEARS OLD IM SO SAD OML
Because it was released 7 years ago duh
It’s Time Maddie
had to watch this at school 5 years ago. just found this channel by accident .
Same!
Emas
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
“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've ruined my life. This is all I can do.
Change your name to: Hexaflexagon Addict.
Improved*
*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
2:43 what went through my mind during Steven Universe: change your mind
||-//💛🖤
nice
Me trying to sleep at 1am:
Hexafelxagons: not today
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 just realised a flexagon is a mobius strip folded uo into a hexagon...wau
Wau!
hi @Michael Darrow
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
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!
If I ever had to hide information, I'd put it in a hexaflexagon
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!