A.P.Polo - "Möbiusband 4.0" - Hamburg-St.Georg (Germany) - Photography / Mixed Media / Digital Art - Long time exposed photograph I took at night out of movement in my hometown Hamburg of the light of skyscrapers. Afterwards it was manipulated with software. A Möbius strip, Möbius band, or Möbius loop , also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary. The Möbius strip has the mathematical property of being unorientable. It can be realized as a ruled surface. Its discovery is attributed to the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858, though a structure similar to the Möbius strip can be seen in Roman mosaics dated circa 200–250 AD. An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip to form a loop. However, the Möbius strip is not a surface of only one exact size and shape, such as the half-twisted paper strip depicted in the illustration. Rather, mathematicians refer to the closed Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any rectangle can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in Euclidean space, and others cannot. A half-twist clockwise gives an embedding of the Möbius strip different from that of a half-twist counterclockwise – that is, as an embedded object in Euclidean space, the Möbius strip is a chiral object with right- or left-handedness. However, the underlying topological spaces within the Möbius strip are homeomorphic in each case. An infinite number of topologically different embeddings of the same topological space into three-dimensional space exist, as the Möbius strip can also be formed by twisting the strip an odd number of times greater than one, or by knotting and twisting the strip, before joining its ends. The complete open Möbius band is an example of a topological surface that is closely related to the standard Möbius strip, but that is not homeomorphic to it. Finding algebraic equations, the solutions of which have the topology of a Möbius strip, is straightforward, but, in general, these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface, having zero Gaussian curvature. A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution. The Euler characteristic of the Möbius strip is zero. Famous depictions of the Möbius strip in art can be found, for example, by M. C. Escher (Möbius strip I and II, 1963) and, more recently, by Gideon Möbius-Sherman. The Argentine feature film Moebius also deals with this theme. The Möbius strip is also a subject of literature: The structure of John Barths short story series "Lost in the Funhouse" is based on the principle of infinity or repetition (e.g. missing centre) of the Möbius strip. The book also comes with a Möbius volume that reflects postmodern literary approaches ("Frame-Tale"). It is labeled: "Once upon a time there was a story that began once upon a time ...". This form of self-reference is typical for so-called strange loops. The poet Erich Fried refers in his poem "Topologik" to the Möbius tape: "I have grasped a Möbius heart that cuts itself into hopeless stripes." Starting in the 1930s, Max Bill created numerous sculptures corresponding to the visual representations of the Möbius strip: e.g. Infinite Loop (1935/37), Continuity (Lake Zurich; 1947, destroyed 1948) or Infinite Loop (Stadtgarten Essen, an der Hohenzollernstraße; 1974). His sculpture Kontinuität (Continuity, 1986), however, does not represent a Möbius strip, contrary to popular belief. The Möbius strip also plays an important role in the novel series Necroscope by the English author Brian Lumley, which has existed since 1986. It is the symbol of some figures, but above all important for the main character Harry Keogh. He learns the ability to travel in time with the help of the so-called Moebius continuum, which behaves similarly to the Moebius strip. The Möbius Strip is also thematized in the Perry Rhodan series, where it forms the three-dimensional model description for the two sides of the n-dimensional universe (Arresum and Paresum). Lars Gustafsson develops the Möbius strip in his novel Frau Sorgedahls beautiful white arms into a Möbius time bottle in which we are trapped. There is nothing outside our life. In the manga series Angel Sanctuary, the fate of the high angel Alexiel and the constant rebirth of his soul into human bodies predestined to a cruel and bloody fate is compared to a Möbius loop. In Michel Houellebecqs 2011 German-language novel Map and Territory, a Möbius strip is engraved on the tombstone of the character Michel Houellebecq. In 2011, the robotics student Aaron Hoover at the University of California, Berkeley, produced a Möbius gear as a technical gadget using 3D printing. The Möbius chess is a variant of the cylinder chess in which one thinks of a twisting of the playing field when "connecting" the long sides. In the video game Mario Kart 8, the Mario Circuit is a Möbius tape. The 8 in the logo also shows a Möbius band. In fashion, Möbius scarves have also been designed. In the play Solaris after Stanislaw Lem by Bettina Bruinier and Katja Friedrich at the Munich Volkstheater (2011) a Möbius band driven by a model car is an important part of the production (stage design: Markus Karner). The logos of Commerzbank and the German cleaning trade show a Möbius strip. The GDR avant-garde band AG. Geige dedicated a song to the Möbius band on the 1989 album Trickbeat. There have been several technical applications for the Möbius strip. Giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time). Möbius strips are common in the manufacture of fabric computer printer and typewriter ribbons, as they let the ribbon be twice as wide as the print head while using both halves evenly. A Möbius resistor is an electronic circuit element that cancels its own inductive reactance. Nikola Tesla patented similar technology in 1894 "Coil for Electro Magnets" was intended for use with his system of global transmission of electricity without wires. The Möbius strip is the configuration space of two unordered points on a circle. Consequently, in music theory, the space of all two-note chords, known as dyads, takes the shape of a Möbius strip; this and generalizations to more points is a significant application of orbifolds to music theory. In physics/electro-technology as: A compact resonator with a resonance frequency that is half that of identically constructed linear coils. An inductionless resistor. Superconductors with high transition temperature. Möbius resonator. In chemistry/nano-technology as: Molecular knots with special characteristics (Knotane, Chirality). Molecular engines. Graphene volume (nano-graphite) with new electronic characteristics, like helical magnetism. A special type of aromaticity: Möbius aromaticity. Charged particles caught in the magnetic field of the earth that can move on a Möbius band. The cyclotide (cyclic protein) kalata B1, active substance of the plant Oldenlandia affinis, contains Möbius topology for the peptide backbone.
A.P.Polo - "Möbiusband 4.0" was created by artist A P Polo in 2018. This art piece , which is part of the Special Relativity - Photograph / Digital Art portfolio, is a Architecture, Digital Art / Computer Art, Photography artwork. The style of this artwork is best described as Abstract, Fine Art, Futurism, Modernism, Symbolism. The genre portrayed in this piece of art is Architecture, Art Brut, Avant-Garde, Celestial / Space, Cityscape, Composition, Conceptual, Environmental art, Fantasy, Mathematics. The artwork was created in Acrylic. The size of the original art is 108 (cms) H x 108 (cms) W.
Words which artist A P Polo feels best describe this work of art are: möbius strip, möbiusband, möbius loop, surface, light, night, photography, digital art, long exposure, photo, euclidean space,
three-dimensional, symbol, shape, loop, abstract, abstract art, wall art, prints, art print, poster, canvas, concept, geometric, icon, infinite,
endless, modern, modern art, m.c escher, line, blue, gold, stripes, logo, motion, math, mathematics, curve, circle, science, physics,
special relativity, creativity, space, dynamic, technology, illusion, pattern, dimension, impossible, contemporary, geometry, universe,
branding, energy, wave, molecular, structure, rotation, form, chemical, symmetry, chemistry, perspective, design element, perception,
simplicity, unlimited, unorientable, ruled surface, August Ferdinand Möbius, Johann Benedict Listing, paper strip, homeomorphic,
boundary, closed curve, chiral object, chiral, topological spaces, square, topology, torus, riemannian metric, poincare, sue goodman,
daniel asimov, klein bottle, real projective plane, conveyor belts, printer, typewriter ribbons, möbius resistor, Nikola Tesla,
music theory, dyads, superconductors, molecular knots, nano-graphite, möbius aromaticity, axis, reflection, geodesics,
configuration space, fiber bundle, cross section, non-orientable wormhole, astrophysics, twisted, alice universe, matter, antimatter,
global geometry, beyond einstein, albert einstein, cosmology, quantum field theory, general relativity, wormhole theory,
einstein-rosen bridge, spacetime, minkowski spacetime, hypersurfaces, schwarzschild wormholes, planck scale, big bang, casimir effect, quantum mechanics, many-worlds interpretation, density matrix, time machine, time travel, interuniversal travel, science-fiction, sci-fi.
A.P.Polo is a visual artist from Spain who lives and works in Hamburg-St.Pauli.
His work includes drawings & painting as well as digital art and photography.