[A person offering a second person a Klein bottle. The second person rejects the Klein bottle. They have a plate of regular three dimensional shapes in front of them. They have picked up a rectangular prism on their fork. In the upper left corner is the text: “No! A responsible adult says no to non-orientable shapes”]
I will eat every shape and you cant stop me
For the betterment of society, I beg you reconsider
NO i will eat a möbius strip like a damn fruit by the foorlt :V
Just a little bottle?
He is offered an interesting shape, but he is not so in-kleined.
I’d appreciate an outside perspective.
But non-orientable geometry allows for the completion of affine space and thus Bezout’s theorem!
where are the trans-dimensional beings supposed to sit in your “responsible” realm there… huh?
You haven’t lived till you comprehended this one! If you peel this entire surface into two surfaces like 2ply toilet paper, this is also a halfway point for one way of turning a sphere inside out, depending on which surface peels which way!
Where can I read more about this?
I think that’s called a Boy’s Surface. There is a different animation of the same object in the Wikipedia article. It’s a disk with a mobius strip glued to its edge, but most articles get too mathsy too quickly for me to understand, so that’s all the information I can provide :3
This is about as accessible as it can get: https://faculty.math.illinois.edu/~jms/Papers/isama/eversions.pdf
The magic happens at the center-point of the surface where the three self-intersections meet. When you ply the surface apart, a tiny cube forms at the triple-point and begins to grow.
Morin’s surface is slightly less complex than splitting the boy’s surface apart, in that sphere eversion halfway model, a trapezoid forms instead of a cube. Inverting a trapezoid in this way is the minimum complexity required to turn a sphere inside out.
Videos I enjoy:
Outside in , which uses a technique different than those above (there’s also a parody out there where the narrators get snarky at eachother)
The optiverse , which uses Morin’s surface mentioned above, but is as ‘smooth’ as mathematically possible.
Here is an alternative Piped link(s): https://piped.video/OI-To1eUtuU
https://piped.video/cdMLLmlS4Dc
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I’m open-source, check me out at GitHub.
Inverting a trapezoid in this way is the minimum complexity required to turn a sphere inside out
that’s fantastic… and i watched the videos, and it still looks like black magic…
very cool