[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”]

  • throwing_handles@lemmy.worldEnglish
    10·
    2 years ago

    image

    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!

      • LordAmplifier@pawb.socialEnglish
        4·
        2 years ago

        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

      • throwing_handles@lemmy.worldEnglish
        1·
        2 years ago

        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.