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In particular, its fundamental group is the same as the fundamental group of a circle, an infinite cyclic group. Therefore, paths on the Möbius strip that start and end at the same point can be distinguished topologically (up to homotopy) only by the number of times they loop around the strip. [16]
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 ...
It follows from this definition and the fact that and are Eilenberg–MacLane spaces of type (,), that the unordered configuration space of the plane is a classifying space for the Artin braid group, and is a classifying space for the pure Artin braid group, when both are considered as discrete groups.
The voluntary referrals relate to separate incidents between December 2019 and March 2022, where children aged 14 to 17 were strip searched. Eight child strip-search cases referred to police ...
The Möbius strip is a surface on which the distinction between clockwise and counterclockwise can be defined locally, but not globally. In general, a surface is said to be orientable if it does not contain a homeomorphic copy of the Möbius strip; intuitively, it has two distinct "sides". For example, the sphere and torus are orientable, while ...
Scotland Yard apologised and said the strip-search at the girl’s school in 2020 without another adult present “should never have happened”. Speaking on LBC radio, Mr Philp said strip ...
Sex Education has reached its fourth and final season, and it has brought along with it a whole new group of characters to fall in love with. In case you need a quick refresh, the kids of Moordale ...
Generalizing the statement above, for a family of path connected spaces , the fundamental group () is the free product of the fundamental groups of the . [10] This fact is a special case of the Seifert–van Kampen theorem, which allows to compute, more generally, fundamental groups of spaces that are glued together from other spaces.