3 ms·

Möbius strip: https://en.m.wikipedia.org/wiki/M%C3%B6bius_strip https://en.m.wikipedia.org/wiki/M%C3%B6bius_strip

• jugg1es 3y ago
  What does boundary mean in this context then? Because the mobius strip has a boundary on the sides even if it is continuous. I guess boundary means an edge in all directions?
  • simonh 3y ago
    A mobius strip is an example of a space that is finite but unbounded in a single direction. A two dimensional plane that is finite but unbounded in all directions is called a Kline bottle, but you can’t build them for real in 3D space, only distorted approximations. You don’t have to do such geometric contortions though. The surface of a sphere is a two dimensional space that is finite but unbounded.
    • ithkuil 3y ago
      Not sure why you need a Mobius strip when an untwisted rectangle with two opposite edges joined (outside of a cylinder) has the same property. Unlike a sphere that would be a flat 2d space (but unlike a sphere it would be unbounded only in one direction)
      • simonh 3y ago
        Donuts are another option. That’s what you get when you join a square at each pair of opposite edges.
        • ithkuil 3y ago
          Indeed the gaussian curvature in a torus is 0.
          • ithkuil 3y ago
            (in 4d only)