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In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE .
He (independently) discovered the properties of the Möbius strip, or half-twisted strip, at the same time (1858) as August Ferdinand Möbius, and went further in exploring the properties of strips with higher-order twists (paradromic rings). He discovered topological invariants which came to be called Listing numbers. [2]
1858: The Möbius strip was discovered independently by the German astronomer–mathematician August Ferdinand Möbius and the German mathematician Johann Benedict Listing in 1858. 1858: Theory of evolution by natural selection – Charles Darwin (discovery about 1840), Alfred Russel Wallace (discovery about 1857–58) – papers published ...
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regions that all touch each other – three along the boundary of the strip and three along its center line – and therefore that graphs that are embedded ...
He is best known for his discovery of the Möbius strip, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space. It was independently discovered by Johann Benedict Listing a few months earlier. [3] The Möbius configuration, formed by two mutually inscribed tetrahedra, is also named after him.
So Brady knew the risk in leaving the comfort of home. And he discovered the upside. Winning his seventh ring in Tampa Bay only enhanced his legacy in New England even if it wasn’t in a Pats jersey.
In another order of ideas, constructing 3-manifolds, it is known that a solid Klein bottle is homeomorphic to the Cartesian product of a Möbius strip and a closed interval. The solid Klein bottle is the non-orientable version of the solid torus , equivalent to D 2 × S 1 . {\displaystyle D^{2}\times S^{1}.}
(Reuters) -Google failed to persuade a federal judge to dismiss a privacy class action claiming it collected personal data from people's cellphones after they switched off a button to stop the ...