Hevea project: H-principle, visualization and applications | Hacker News Reader

Hevea project: H-principle, visualization and applications

hevea-project.fr

56 pointssriku12 comments

Big name: John Nash (he's actually more famous for his embedding theorems in the math community)

Not so big name: Candes (coauthor with Terence Tao of that compressed sensing paper.)

This is their pure math roots. And I think this implies an overlooked class of (almost foldable) origami.

http://hevea-project.fr/ENPageToreDossierDePresse.html

The embedding of the flat torus is a mesmerizing construction. Every time you see it, you are left speechless by its beauty.

So I guess it has nothing to do with http://hevea.inria.fr

Is there a reason why French people like that name so much?

It seems to be, roughly, a French word for latex rubber. Hence why it's used for a LaTeX tool, and for a study on deformed surfaces.

Hevea is the name of the tree producing rubber. (Actually the genus)[0]

[0]https://en.wikipedia.org/wiki/Hevea

Someone please explain us:

- what the heck are we seeing

- why is a twisted 3d object such a big deal

- what are the applications

Click on the headline to see an explanatory paragraph. (Terrible design. Why is it hidden?)

Also, there is a detailed explanation on the site here: http://hevea-project.fr/ENPageToreDossierDePresse.html

It's hidden behind a link labeled "Folder", which doesn't really make sense in English (it's a direct translation of French "dossier").

I've read the explanation of the construction of the flat torus on TF-web-site. But I fail to see what kind of consequences this construction has. Does it open the way to new solutions to old problems, have practical applications or is it, for the moment, "just" a nice mathematical object ? (I'll be 100% satisfied with the later, it's incredibly mind bending)

Thanks. This should really be the featured link.

OK. I think I've got it. It's a way to map a 2D square to 3 dimensions without distorting distance. Is that right?

A simple torus mapping stretches distance in the x direction depending on whether you're on the inside or outside of the torus - and the wrinkles fix this.

(IANAM if that wasn't obvious)

For people who don't want to read the full explanation: This is showing a distance-preserving embedding of a torus and other shapes in 3 dimensions. The simple method of embedding the torus as a doughnut shape requires stretching it, which means distances are not preserved. For example, the inner circumference is smaller than the outer one. But it turns out you can add corrugations of varying amplitude to counteract this effect. As you might expect, it requires an infinite sequence of ever-smaller layers of corrugations to exactly offset the stretching effect and achieve exact preservation of all distances in all directions, but just like constructing a fractal, we can generate the first few steps and stop once the corrugations of the next step would be too small to see. That's what the visualizations on this site are.

Source code link is not working.

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