# Definitions for orientabilityori·entabil·i·ty

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1. orientabilitynoun

The condition of being orientable

### WikipediaRate this definition:0.0 / 0 votes

1. Orientability

In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space. Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. A generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.

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1. Orientability

In mathematics, orientability is a property of surfaces in Euclidean space measuring whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance. More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is orientable if a two-dimensional figure such as in the space cannot be moved around the space and back to where it started so that it looks like its own mirror image . The notion of orientability can be generalised to higher dimensional manifolds as well. A manifold is orientable if it has a consistent choice of orientation, and a connected orientable manifold has exactly two different possible orientations. In this setting, various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.

### Numerology

1. Chaldean Numerology

The numerical value of orientability in Chaldean Numerology is: 1

2. Pythagorean Numerology

The numerical value of orientability in Pythagorean Numerology is: 6

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"orientability." Definitions.net. STANDS4 LLC, 2023. Web. 28 Nov. 2023. <https://www.definitions.net/definition/orientability>.

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