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If you make this bowl, it will have two surfaces, with no way to get from one side to the other.
by TobbenTM 11y ago
If you make this bowl, it will have two surfaces, with no way to get from one side to the other.
- bambax 11y agoWell, I'm not sure about that. The top of my bowl is the top-half of a doughnut if you will: it really does not seem to have an edge. At what point does an "edge" appear?
- peterfirefly 11y agoBut you do have two surfaces: inside and outside. The Klein bottle only has one.
- glomph 11y agoIt has an inner surface and an outer surface, the same as a sphere. They didn't say it had an edge.
- bambax 11y agoYes, in the video I'm talking about https://www.youtube.com/watch?v=AAsICMPwGPY https://www.youtube.com/watch?v=AAsICMPwGPY he says that a bootle has an edge (~3'40). A sphere does not have an "inner surface", it has just one surface. So does a potato. If you go from sphere to potato to bowl, when does an edge appear and does it have to appear, is my question.
- geon 11y agoWell. A bottle is topologically equivalent to a solid sphere. It only has one surface. The inside and outside of a bottle is just by convention. Usually you would say something is inside the bottle if it is past the opening. (As he says in the video.) So your example with the bowl-shaped "sphere" is correct. There's no clear limit when a bottle has an inside and an outside.
- chii 11y agothe object that have only one surface, but no edge, is a klein bottle. A sphere (or if you will, a ball pressed into a bowl shape) has two surfaces - the outer one, and the "inner" one (where the "inner one" is the one you cannot reach from the outer one, as tho the surface is infinitely thin, and the bowl/sphere is made of hollowness.