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Hexaflexagons [video] (2012)

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Re: Hexaflexagons [video] (2012)

#2

Post by mgdlbp »

A recent submission[1] reminds me of the series on flexagons—folded paper with more than two faces that can be swapped via a 'flexing' operation—by Vi Hart, whose videos on mathematics were quite popular on YouTube around ten years ago.

https://www.youtube.com/user/Vihart/videos?sort=p, https://hn.algolia.com/?query=vi%20hart

[1] 'folding' in a different sense: How to fold a Julia fractal (2013) - https://news.ycombinator.com/item?id=32209192

Re: Hexaflexagons [video] (2012)

#4

Post by Jtsummers »

notRobot wrote: post #3

I know about Vi Hart but hadn't seen this series before, I just watched the first two videos and my mind is so blown right now, this is incredible. I love fun math stuff like this.

If you liked this, you ought to check out Gardner's articles themselves:

https://en.wikipedia.org/wiki/Martin_Gardner_bibliography#%2... - That's a list of the books (and on that page many other things) collecting Gardner's Scientific American "Mathematical Games" articles.

https://www.cambridge.org/us/academic/subjects/mathematics/s... - First 4 of the reprints available here (or a bookseller of your choice).

Re: Hexaflexagons [video] (2012)

#5

Post by Klaster_1 »

Are there any practical applications to this, like making nanoscale structures that can change particle or surface properties? What's the smallest possible structure that enables bending? This looks like one of those mundane problems that yields unexpectedly impactful applications, like moiré pattern and magic angle graphene.

Re: Hexaflexagons [video] (2012)

#7

Post by mdp2021 »

I built so many, as a child, after reading Martin Gardner. Six faces for the basic ones, then many more. I used the tape of calculators with mechanical printing.

Edit: looking for the original article from Martin Gardner; meanwhile: the submitted video was commented by the Scientific American (the original container) - https://blogs.scientificamerican.com/observations/flexagon-b...

The original article was Flexagons // In which strips of paper are used to make hexagonal figures with unusual properties, published on December 1, 1956. The Scientific American has it online, but paywalled.

Found it:

https://archive.org/details/martingardnerthecolossalbookofma...

in Martin Gardner - The Colossal Book Of Mathematics (page 385)

Re: Hexaflexagons [video] (2012)

#8

Post by mgdlbp »

mgdlbp wrote: post #2

A recent submission[1] reminds me of the series on flexagons—folded paper with more than two faces that can be swapped via a 'flexing' operation—by Vi Hart, whose videos on mathematics were quite popular on YouTube around ten years ago. https://www.youtube.com/user/Vihart/videos?sort=p , https://hn.algolia.com/?query=vi%20hart [1] 'folding' in a different sense: How to fold a Julia fractal (2013) - https://news.ycomb…

Interesting— Vi Hart was a PI for YC Research's HARC (known mostly for Bret Victor's Dynamicland) – small world

https://hn.algolia.com/?query=harc

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