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Lot of people seeming to miss that point here!


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I don’t think that really narrows it down, but this is certainly one of the math animations of all time!
This animation and explanation is really good!! The studio, which is guess was new at the time, was called Pixar. According to the credits, one of the animators there shares a last name with one of the mathematicians who developed this method (Thurston).


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I’ve really been looking forward to this! This announcement post is really sweet, and makes me glad for all the folks who worked on it.


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Actually my first time; I had to order them just for this, and they’re great! Now I have extras ready for the next project.
7 hellhounds howling
No, you’re supposed to buy a loaf, use 1/3 of it before it goes bad, throw away the rest, and buy another loaf.


Thanks; that worked! I was a little worried about the extra steps for my Nvidia card, but it was fine. Cosmic seems cool so far.


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Loves Ukraine though.
Freecad +1
WAIT !
I think each person has to recognize that there is a time/energy cost to get out of enshittification hell, and then decide how much they’re willing to pay. If the answer for you is at least “an afternoon of video tutorials”, then Freecad will be fine for you. It’s a complicated tool that you need some help learning; that’s ok. It won’t become your new hobby.
If you don’t want to pay that cost, that’s understandable. If you feel mad that there is a cost at all, that’s ok too. That’s how enshittification works, and it sucks. As I said, each person will have to decide whether and how much they’re willing to pay to get out of it.
Anyway, the MangoJelly tutorials in YouTube are really excellent, and will have you up and running in a few hours at most. (My CAD needs are also very basic, and I was done after the first two parts, 30 min each.) For following along, I would recommend just using the main version, so that it matches his tutorial exactly, and do the steps as he shows you. It feels dumb, but it’s such a fast way to learn. You can decide later if you want to switch to one of the other branches, depending on what features you care about or what annoys you most.
https://www.youtube.com/playlist?list=PLiGNkhS8RKFIJWGj1ad8wRVVCLBnF_13g
Here’s one of his later videos about tracing from a photo, but I haven’t watched it:
https://youtu.be/xQcDoAhmoa8?si=MkdyXVtATiNWesJ4
You can do it!
I had the same realization. I spent 3-4 hours fiddling with different settings, with no impact, and then 1 hour drying did the trick!!
For each finite dimension n (1, or 2, or 3, etc…), the sphere in dimension n can’t be contracted because of that empty n-dimensional space it surrounds. But that same sphere is the “equator” of the sphere in the next higher dimension, n+1. There, the n-dimensional equator can contract along one of the hemispheres, to a pole. But then that whole (n+1)-dimensional sphere still isn’t contractible, because of the (n+1)-dimensional space it surrounds.
BUT the (n+1)-dimensional sphere can contract along one of the hemispheres in the (n+2)-dimensional sphere. And so on.
For any particular finite dimension n, there is an n-dimensional obstruction to contracting the sphere in that dimension. But if you go all the way to infinitely-many dimensions, there is no obstruction that ever stops contractibility of the infinite-dimensional sphere.