Preview

The Klein Bottle: Non-Orientable Surface

Good Essays
Open Document
Open Document
478 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
The Klein Bottle: Non-Orientable Surface
In mathematics, the Klein bottle ([klaɪ̯n]) is a non-orientable surface, informally, a surface (a two-dimensional manifold) with no identifiable "inner" and "outer" sides. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a two-dimensional surface with boundary, a Klein bottle has no boundary. (For comparison, a sphere is an orientable surface with no boundary.) The Klein bottle was first described in 1882 by the German mathematician Felix Klein. In physics/electro-technology: * 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 In chemistry/nano-technology: * 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

You May Also Find These Documents Helpful

Related Topics