The Klein bottle was first described in 1882 by the German mathematician Felix Klein.
* as compact resonator with the resonance frequency which is half that of identically constructed linear coils * as inductionless resistance.
* as superconductors with high transition temperature
* as molecular knots with special characteristics (Knotane) * as molecular engines
* as graphene volume (nano-graphite) with new electronic characteristics, like helical magnetism. * In a special type of aromaticity: Möbius aromaticity * Charged particles, which were caught in the magnetic field of the earth, can move on a Möbius band. * The cyclotide (cyclic protein), active substance of the plant Oldenlandia affinis, contains Möbius topology for the peptide backbone.
In mathematics, a cross-cap is a two-dimensional surface that is topologically equivalent (i.e. homeomorphic) to a Möbius strip. The term ‘cross-cap’, however, often implies that the surface has been deformed so that its boundary is an ordinary circle.
A cross-cap that has been closed up by gluing a disc to its boundary is an immersion of the real projective plane. Two cross-caps glued together at their boundaries form a Klein bottle.
In chemistry, a molecular knot, or knotane, is a mechanically-interlocked molecular architecture. Examples of naturally formed knotanes are DNA and certain proteins. Lactoferrin has an unusual biochemical reactivity compared to its...