Hexaflexagons! The miracle of the inside-out hexagon with many, many sides

The incomparably great Vihart continues her Doodling in Math Class video series with a history and demonstration of the miraculous Hexaflexagon, a simple-to-fold paper hexagon that contains several iterations of itself, which can be found by turning it inside-out over and over again. Sure to delight, inform, entertain, and mystify!

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.

Hexaflexagons (Thanks, Fipi Lele!)

I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.

MORE: extreme fidgeting • geometry • happy mutants • math • papercraft • videos • youtube

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http://profiles.google.com/srharvey Shane Harvey

Well there go any chance of me being productive today….
bcsizemo

I think I’m more intrigued by the yellow finger nails (on the left hand) and miss matched sweater sleeves…

Plus it also reminds me of my Rubik Magic:
https://www.youtube.com/watch?v=dxW99wWwpwY
Sxe

I first played with these as a kid in the ’80s when I learned about them from the following incredible kids’ activity book:

http://www.amazon.com/Best-Ever-Indoor-Games-McToots-adventure/dp/0668062959/ref=la_B001HPJNH8_1_1?ie=UTF8&qid=1349235468&sr=1-1

The reason hexaflexagons do all that weird stuff is that they are flattened-out Mobius strips.
- noah django
  
  I was totally gonna say Mobius strip! Vindication!!!!!!
Charlie B

A wonderful thing! In fact, after watching several of them I am suspecting all her videos are wonderful things.

Thanks, Cory!
http://twitter.com/buckdoyle Buck Doyle

I am sadly not surprised that 40% of the comments (at the time of this writing) sexualise the presenter.
- http://www.nathanhornby.com/ Nathan Hornby
  
  I spotted one.
  
  And it said ‘brains are hawt’.
  
  Concern troll is concerned.
  - zefuture
    
    It’s not trolling if it’s true.
    
    And in case you missed it the other totally off-topic comment is « I think I’m more intrigued by the yellow finger nails (on the left hand) and miss matched sweater sleeves… »
    Talking about the video-maker’s clothes when the video is about amazing math, is unnecessary and I bet it wouldn’t have happened if ViHart was a guy. That is sexism.
    - http://www.nathanhornby.com/ Nathan Hornby
      
      Seriously? Pointing out the obviously unusual mismatch of sleeves and the fact that there’s yellow nail polish on one hand is sexualising the video maker? I noticed this too, I must be a rapist.
      
      http://www.youtube.com/watch?v=2Z4m4lnjxkY
      
      “Talking about the video-maker’s clothes when the video is about amazing math, is unnecessary and I bet it wouldn’t have happened if ViHart was a guy. That is sexism.”
      
      If it were a guy, Antinous would have been drooling in the comments before anyone even got a shot in. You do nothing for the plight of over sexualised women by making an issue out of absolutely nothing.
      
      Also we were talking about over sexualising, not sexism. For what it’s worth, this is neither. Super secret pro-tip: human beings are often attracted to each other – sometimes even via their personality!
    - Guest
      
      deleted
    - SamSam
      
      I was waiting for, and disappointed by, the “if I were 30 years younger” comment, but I agree with Nathan that you’re reaching if you find the comment mentioning her nails polish color to be sexualizing. If it were a guy wearing nail polish, people would probably mention it as well…
      - sarahnocal
        
        Actually if it were guys that wore nail polish instead of girls I doubt if anyone would mention anything.
Antinous / Moderator

I used to have a cardboard thing with photos of galaxies on it that could be manipulated like this, only larger and more complicated. Anybody know what I’m talking about? It was c.1990.
CH

Vi Hart rules! I absolutely love all her videos. Not only is she presenting math in a fun way, but her enthusiasm for it is so infectious!
AllyPally

Ah, I used to play with hexahexaflexagons after I read how about them in a book by Martin Gardner. Hours of fun, especially if you use pictures rather than colours. Thanks, boingboing. I’m going to have to make one today.
Laurence Brothers

Damn, I woke up this morning thinking about flexagons for the first time in many years. And what do I see on the front page?
alfanovember

If I were a Bond Villain, I’d offer Vi Hart her own tropical island with monkey butlers and a hammock district and a zeppelin to fly her to conferences if only she would tutor my kids in person.