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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 directio
by 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 agoNot 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)