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- Orthant abstract "In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In general an orthant in n-dimensions can be considered the intersection of n mutually orthogonal half-spaces. By permutations of half-space signs, there are 2n orthants in n-dimensional space.More specifically, a closed orthant in Rn is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive. Such a subset is defined by a system of inequalities:ε1x1 ≥ 0 ε2x2 ≥ 0 · · · εnxn ≥ 0,where each εi is +1 or −1.Similarly, an open orthant in Rn is a subset defined by a system of strict inequalitiesε1x1 > 0 ε2x2 > 0 · · · εnxn > 0,where each εi is +1 or −1.By dimension:In one dimension, an orthant is a ray.In two dimensions, an orthant is a quadrant.In three dimensions, an orthant is an octant.John Conway defined the term n-orthoplex from orthant complex as a regular polytope in n-dimensions with 2n simplex facets, one per orthant.".
- Orthant thumbnail Cartesian_coordinates_2D.svg?width=300.
- Orthant wikiPageID "1283725".
- Orthant wikiPageRevisionID "571608543".
- Orthant hasPhotoCollection Orthant.
- Orthant subject Category:Euclidean_geometry.
- Orthant subject Category:Linear_algebra.
- Orthant comment "In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In general an orthant in n-dimensions can be considered the intersection of n mutually orthogonal half-spaces. By permutations of half-space signs, there are 2n orthants in n-dimensional space.More specifically, a closed orthant in Rn is a subset defined by constraining each Cartesian coordinate to be nonnegative or nonpositive.".
- Orthant label "Orthant".
- Orthant label "Orthant".
- Orthant label "Ортант".
- Orthant sameAs Orthant.
- Orthant sameAs m.04p_2y.
- Orthant sameAs Q2714507.
- Orthant sameAs Q2714507.
- Orthant wasDerivedFrom Orthant?oldid=571608543.
- Orthant depiction Cartesian_coordinates_2D.svg.
- Orthant isPrimaryTopicOf Orthant.
