In math there is a geometric-topologic construction which is a source of fun and surprises. It is surface. It is a two dimensional object which can be embed in the three dimensional euclidean space, . It is a model to illustrate the concept of twisted bundle. In fact an -bundle, an interval bundle over the circle. The möbius band or möbius strip is the principal element to construct all the non orientable surfaces: the projective plane; the Klein bottle; ; ,… etc.
What happens if we remove the core central simple closed curve? look at the 2nd image.
I had spended many eons to popularize the symbol
The möbius band is employed to manufature many exotic non orientable three dimensional spaces. By the record, talking about 3d spaces: isn’t the only one.
For example is a solid Klein bottle and an innocent quiz is: can you see what is the bounding surface of this -bundle?
For a bundle of additional properties check this link
The images were rendered in Mathematica v.5
La siguiente figura te explica como ver una construcción tridimensional que involucra a la banda…
Aquí estamos usando para la superficie de género dos no orientable,,