I can’t comprehend it
In: Mathematics
NOTE: this explanation assumes the reader knows what a Klein bottle is.
It has to exist in 4 spatial dimensions. If it is just 3 dimensional, then the neck has to intersect the body of the bottle. By definition, the bottle can’t intersect itself, so in order for the surface to be completely continuous, it has to ‘jump’ over the 3D surface in the direction of a 4th dimension.
I don’t know if that made any sense — it’s a difficult thing to explain with just text. Think about a 2D figure ‘8’. In 2D, the middle of the 8 intersects itself. But you could imagine it in 3D as a string, where the string jumps over itself in the 3rd dimension. The same thing is happening with the ‘intersection’ in the Klein bottle, only it jumps over itself in a 4th dimension.
Latest Answers