Too Many Triangles - Numberphile

How many triangles are too many? Featuring Henry Segerman from Oklahoma State University.
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NUMBERPHILE

Videos by Brady Haran

[ryPish]

This is the best and most intuitive way to teach people about hyperbolic surfaces, yay 3D printing!

[GelidGanef]

Oh man, I used to draw those little 7-triangle things on my school notebooks!

Just go out farther and farther from the center, making smaller and smaller triangles just as equilateral as you possibly can. Until suddenly you hit a hard limit and you just cant fit anymore in, or you can't see them anymore because they get too small.

It makes a cool design. I'd love to have a 3d printed version to play with now.

[magnusdagbro]

A geodesic dome like that would be a great tool to teach school kids about map projections, and how you can't trust a world map.

Print a world map on one and place it on a matching sphere so it looks like a globe, then let the kids play with the "carpet" of triangles and see how you can never make it flat without distorting something.

[Snootypriss]

I like everyone, but Segerman's my favorite numberphile guest. I like how he explains stuff and I like the 3D printing models.

[Hecatonicosachoron]

You can get closed hyperbolic surfaces, analogous to a sphere. They just have at least two holes in them - but no boundaries.
You can even tile them with regular polygons, if you feel so inclined. It's a great puzzle to think about! It also comes with profound group theoretical consequences.

[stormsurge]

That looks like the cloth my grandma has on her TV

[Snaake]

The fractal-ish nature of the 7- and 8-triangle surfaces and especially the "geodesic dome" version of the 7-triangle surface reminded me of the way the surface of kale, some other cabbages and lettuce are wrinkled (I think he actually mentioned lettuce earlier on in the video). Another natural approximation of a mathematical concept, much like Romanesco broccoli?

[antoineroquentin]

"Triangles are happier in groups. They're like sheep. They get sad and lonely by themselves"
--ViHart

[ganaraminukshuk]

And here I am thinking about Vihart just saying "triangles" constantly and "hyperbolic doily" takes the cake.

[NA-mgeb]

The idea that keeps going through my head with this is that if you could find some way to keep small miniatures attached (velcro? magnets?) even when the area they're in is crinkled up, then these would make excellent battle mats for Call of Cthulhu

[tibimose]

I finally found out why in my grandma's time, there was a hype with "mileuri" (it's a romanian word for something that looks like the 6 triangle flat one, that you put on furniture for decoration). The fascination with maths was real

[whatthefunction]

*"hyperbolic doily"* is my band's name.

[danielstephenson]

Henry has created what I can only describe as the 'forbidden doily'

[joelshewmaker]

I must say, I didn't expect him to name drop the Triforce.

[AaronRClark]

I had just come back to watching numberphile after a 6 month hiatus. I enjoy this Henry Segerman.

[HontubeYT]

3:13 Is my favourite moment in the video as it gets me laughing everytime.

[null]

I don't know why but I love when numberphile uploads videos about geometry

[zlac]

You can do this quite nicely in software called "magic tiles", it's a software that does all sorts of Rubik's cube equivalents in all kinds of spaces, even hyperbolic, really nice stuff!

[Rurexxx]

This guy is a 3D printing wizard. Seriously, what a skill and knowledge!

[MultiSteveB]

3-5 = "spheres"
6 = "plane"
7-8 = "quantum foam model"?