3 ms·
Someone please explain us: - what the heck are we seeing - why is a twisted 3d object such a big deal - what are the applications
by whage 9y ago
Someone please explain us:
- what the heck are we seeing
- why is a twisted 3d object such a big deal
- what are the applications
- pavlov 9y agoClick 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 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").
- andybak 9y agoOK. 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)
- wiz21c 9y agoI'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)
- tom_mellior 9y agoThanks. This should really be the featured link.
- rcthompson 9y agoFor 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.