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In the mathematical field of [[algebraic topology]], the '''orientation sheaf''' on a [[manifold]] ''X''<!-- or some reasonable f-dim space to whic ...ted manifold|oriented]], one can always integrate a density, regardless of orientation or orientability; there is the integration map: ...

{{Short description|Generalization of an orientation of a vector space}} ...entation of ''E'' means: for each fiber ''E''_''x'', there is an orientation of the vector space ''E''_''x'' and one demands that each trivial ...

...lues to vertices with larger objective values, the result is a unique sink orientation. Thus, unique sink orientations can be used to model [[linear program]]s as ...blem]]s by {{harvtxt|Stickney|Watson|1978}} and it was termed "unique sink orientation" in 2001 {{harv|Szabó|Welzl|2001}}. ...

In [[geometry]], a '''polygon with holes''' is an area-connected planar [[polygon]] with | title = An Introduction To The Geometry Of <math>N</math> Dimensions ...

...sbn|0-471-41825-0}}</ref> including [[elliptic geometry]] and [[hyperbolic geometry]]. In the latter case, [[hyperbolic motion]]s provide an approach to the su ...slation]]s and [[rotation]]s that preserve the [[orientation (mathematics)|orientation]] of a [[Chirality (mathematics)|chiral]] [[shape]]. ...

...ometric definition of a closed line segment: the [[intersection (Euclidean geometry)|intersection]] of all points at or to the right of {{mvar|A}} with all poi {{General geometry}} ...

...]] of the region is a [[simple curve]], the signed area also indicates the orientation of the boundary. ...1&ndash;369}} Greek geometers often compared planar areas by [[quadrature (geometry)|quadrature]] (constructing a [[square]] of the same area as the shape), an ...

...are rotated to the Cartesian coordinate system (E, N, Z).|thumb|300x300px|Geometry of the Galperin configuration: three orthogonal vectors (U, V, W) are rotat ...ty to build smaller packages (i.e., instruments) compared to the Cartesian orientation,<ref name=":1" /> which makes the Galperin configuration especially applica ...

[[Group action (mathematics)|Group action]]s are central to [[Riemannian geometry]] and defining [[Orbit (control theory)|orbits (control theory)]]. ...edical images]]; the anatomical shapes are submanifolds of [[differential geometry]] consisting of points, curves, surfaces and subvolumes,. ...

The '''Tienstra formula''' is used to solve the [[Resection (orientation)|resection]] problem in [[surveying]], by which the location of a given poi [[Category:Euclidean plane geometry]] ...

...n-spherical objects, the distance of closest approach is a function of the orientation of the objects, and its calculation can be difficult. The maximum [[packin ...ere]]. For other [[anisotropic]] objects, the excluded volume depends on orientation, and its calculation can be surprising difficult.<ref>Forces, Growth and Fo ...

...ransformations — Some geometry of Minkowski (2+1)-space|journal=Journal of Geometry|language=en|volume=52|issue=1|pages=74–90|doi=10.1007/BF01406828|s2cid=1225 ...inder are in a natural [[one-to-one correspondence]] with oriented [[line (geometry)|lines]] on the plane. ...

In [[differential geometry]], an '''isotropic vector field''' is a concept that refers to a [[vector f ...ts uniform behavior across the manifold. This means that its magnitude and orientation are consistent in all directions at any given point. ...

{{Short description|Geometry calculation}} ...tic geometry]] description of a [[Line (geometry)|line]] and a [[Cylinder (geometry)|cylinder]] in 3d space. ...

...the [[Orientability|orientation]] of its planar embedding, and another six orientation-reversing symmetries.<ref name=marcusanu/> ...an [[isometric embedding]] from the graph into a 12-dimensional [[taxicab geometry]]. The 26-fullerene graph is one of only five fullerenes with such an embed ...

...id transformation by requiring that the transformation also preserve the [[orientation (mathematics)|handedness]] of objects in the Euclidean space. (A reflection In dimension two, a rigid motion is either a [[translation (geometry)|translation]] or a [[rotation (mathematics)|rotation]]. In dimension three ...

== Use in geometry == ...) p. 24</ref><ref>''[https://books.google.com/books?id=HfFYvQEACAAJ Modern geometry of the point, straight line, and circle: an elementary treatise]'' by [[Joh ...

...his number depends on the size and shape of the bodies, and their relative orientation to each other. Hadwiger's theorem asserts that every [[Valuation (geometry)|valuation]] on convex bodies in <math>\mathbb{R}^n</math> that is continuo ...

{{Short description|Concept in geometry}} In algebraic geometry, a '''localized Chern class''' is a variant of a [[Chern class]], that is d ...

...chmid-Faktor}} or {{langx|de|Schmid'scher Orientierungsfaktor|lit=Schmid's orientation factor|label=none}}.<ref name=merkel-thomas>{{cite book|last=Merkel|first=M ...{mvar|σ}}) multiplied by the cosine of the angle with the vector [[Normal (geometry)|normal]] to the glide plane ({{mvar|φ}}) and the cosine of the angle with ...