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25-529: [REDACTED] Look up flat in Wiktionary, the free dictionary. Flat or flats may refer to: Architecture [ edit ] Apartment , known as a flat in the United Kingdom, Ireland, and other Commonwealth countries Arts and entertainment [ edit ] Flat (music) , a symbol ( ♭ ) which denotes a lower pitch Flat (soldier) ,

50-1061: A character in some Levi's commercials Flat Stanley , namesake of an American children's book series Groups [ edit ] FLATS or First Lady Astronaut Trainees , American women who underwent NASA Project Mercury physiological screening tests Other uses [ edit ] Flat (gridiron football) , the area of the gridiron football field Flat butterflies or flats, certain skipper butterfly genera in subfamily Pyrginae : Calleagris (scarce flats), Celaenorrhinus of tribe Celaenorrhinini; Eagris , and Tagiades (water flats, snow flats), of tribe Tagiadini Flats (USPS) , an oversized letter Optical flat , an extremely flat piece of glass See also [ edit ] All pages with titles beginning with Flat All pages with titles containing Flat The Flat (disambiguation) , including "The Flats" Flat Earth (disambiguation) Flatbed (disambiguation) Flatten (disambiguation) Flattening Flatness (disambiguation) Topics referred to by

75-1061: A character in some Levi's commercials Flat Stanley , namesake of an American children's book series Groups [ edit ] FLATS or First Lady Astronaut Trainees , American women who underwent NASA Project Mercury physiological screening tests Other uses [ edit ] Flat (gridiron football) , the area of the gridiron football field Flat butterflies or flats, certain skipper butterfly genera in subfamily Pyrginae : Calleagris (scarce flats), Celaenorrhinus of tribe Celaenorrhinini; Eagris , and Tagiades (water flats, snow flats), of tribe Tagiadini Flats (USPS) , an oversized letter Optical flat , an extremely flat piece of glass See also [ edit ] All pages with titles beginning with Flat All pages with titles containing Flat The Flat (disambiguation) , including "The Flats" Flat Earth (disambiguation) Flatbed (disambiguation) Flatten (disambiguation) Flattening Flatness (disambiguation) Topics referred to by

100-603: A commune in the French region of Auvergne Flat Island (disambiguation) , in various places Flat Islands (disambiguation) , in Canada and Antarctica Flat River (disambiguation) , in the United States and Canada Mathematics and geometry [ edit ] Flat (geometry) , the generalization of lines and planes in an n -dimensional Euclidean space Flat (matroids) , a further generalization of flats from linear algebra to

125-474: A line in three-dimensional space is determined by two distinct points or by two distinct planes. However, the lattice of all flats is not a distributive lattice . If two lines ℓ 1 and ℓ 2 intersect, then ℓ 1 ∩ ℓ 2 is a point. If p is a point not lying on the same plane, then (ℓ 1 ∩ ℓ 2 ) + p = (ℓ 1 + p ) ∩ (ℓ 2 + p ) , both representing a line. But when ℓ 1 and ℓ 2 are parallel, this distributivity fails, giving p on

150-399: A plane, while a pair of linear equations can be used to describe a line. In general, a linear equation in n variables describes a hyperplane, and a system of linear equations describes the intersection of those hyperplanes. Assuming the equations are consistent and linearly independent , a system of k equations describes a flat of dimension n − k . A flat can also be described by

175-425: A race Geography [ edit ] Landforms [ edit ] Flat (landform) , a relatively level area within a region of greater relief Mudflat , intertidal wetland with a substrate of fine sediments Bodies of water [ edit ] Flat, a shallow water area in the context of boating , fishing or marine biology , often used in plural form Brewster Flats , an area of Cape Cod Bay off

200-696: A shoreline where the land descends gradually into the sea Places [ edit ] United States [ edit ] Flat, Alaska , a census-designated place Flat, Kentucky , an unincorporated community Flat, Missouri , an unincorporated community Flat, Texas , an unincorporated community Flat Brook , a tributary of the Delaware River in Sussex County, New Jersey Flats, Nebraska , United States Flats, West Virginia , an unincorporated community Forest Lake Area Trail System , Missouri Other [ edit ] Flat, Puy-de-Dôme ,

225-415: A substrate of fine sediments Bodies of water [ edit ] Flat, a shallow water area in the context of boating , fishing or marine biology , often used in plural form Brewster Flats , an area of Cape Cod Bay off the shore of Massachusetts, U.S. Kentish Flats Offshore Wind Farm , off the coast of Kent, England Rhyl Flats , a wind farm off the coast of North Wales Flat coast ,

250-521: A symbol ( ♭ ) which denotes a lower pitch Flat (soldier) , a two-dimensional toy soldier made of tin or plastic Flat (theatre) , a flat piece of theatrical scenery Flat, a leading type of wordplay, as identified by the National Puzzlers' League Flat! (2010), an Indian film Flats (band) , an English band Flats (comics) , the first stage in the comic coloring process Footwear [ edit ] Flats, footwear which

275-490: A system of linear parametric equations . A line can be described by equations involving one parameter : while the description of a plane would require two parameters: In general, a parameterization of a flat of dimension k would require k parameters, e.g. t 1 , …,  t k . An intersection of flats is either a flat or the empty set . If each line from one flat is parallel to some line from another flat, then these two flats are parallel . Two parallel flats of

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300-446: A tributary of the Delaware River in Sussex County, New Jersey Flats, Nebraska , United States Flats, West Virginia , an unincorporated community Forest Lake Area Trail System , Missouri Other [ edit ] Flat, Puy-de-Dôme , a commune in the French region of Auvergne Flat Island (disambiguation) , in various places Flat Islands (disambiguation) , in Canada and Antarctica Flat River (disambiguation) , in

325-652: A two-dimensional toy soldier made of tin or plastic Flat (theatre) , a flat piece of theatrical scenery Flat, a leading type of wordplay, as identified by the National Puzzlers' League Flat! (2010), an Indian film Flats (band) , an English band Flats (comics) , the first stage in the comic coloring process Footwear [ edit ] Flats, footwear which is not high-heeled Ballet flats , derived from ballet shoes, for casual wear as well as dancing Ballet shoes (also known as ballet slippers), often referred to as "flats" or "flat shoes" Racing flats , lightweight shoes used primarily for running

350-426: Is a manifold and an algebraic variety , and is sometimes called a linear manifold or linear variety to distinguish it from other manifolds or varieties. A flat can be described by a system of linear equations . For example, a line in two-dimensional space can be described by a single linear equation involving x and y : In three-dimensional space, a single linear equation involving x , y , and z defines

375-462: Is different from Wikidata All article disambiguation pages All disambiguation pages flat [REDACTED] Look up flat in Wiktionary, the free dictionary. Flat or flats may refer to: Architecture [ edit ] Apartment , known as a flat in the United Kingdom, Ireland, and other Commonwealth countries Arts and entertainment [ edit ] Flat (music) ,

400-401: Is different from Wikidata All article disambiguation pages All disambiguation pages Flat (geometry) In an n -dimensional space , there are k -flats of every dimension k from 0 to n ; flats one dimension lower than the parent space, ( n  − 1) -flats, are called hyperplanes . The flats in a plane (two-dimensional space) are points , lines , and

425-451: Is not high-heeled Ballet flats , derived from ballet shoes, for casual wear as well as dancing Ballet shoes (also known as ballet slippers), often referred to as "flats" or "flat shoes" Racing flats , lightweight shoes used primarily for running a race Geography [ edit ] Landforms [ edit ] Flat (landform) , a relatively level area within a region of greater relief Mudflat , intertidal wetland with

450-738: The United States and Canada Mathematics and geometry [ edit ] Flat (geometry) , the generalization of lines and planes in an n -dimensional Euclidean space Flat (matroids) , a further generalization of flats from linear algebra to the context of matroids Flat module in ring theory Flat morphism in algebraic geometry Flat space , a space with zero curvature Flat sign, for its use in mathematics; see musical isomorphism , mapping vectors to covectors People [ edit ] Nickname [ edit ] Earl "Flat" Chase (1910–1954), Canadian baseball player Flat Walsh (1897–1959), Canadian ice hockey goaltender Fictional characters [ edit ] Flat Eric ,

475-482: The context of matroids Flat module in ring theory Flat morphism in algebraic geometry Flat space , a space with zero curvature Flat sign, for its use in mathematics; see musical isomorphism , mapping vectors to covectors People [ edit ] Nickname [ edit ] Earl "Flat" Chase (1910–1954), Canadian baseball player Flat Walsh (1897–1959), Canadian ice hockey goaltender Fictional characters [ edit ] Flat Eric ,

500-543: The minimal flat which contains them, of dimension at most k 1 + k 2 + 1 . If two flats intersect, then the dimension of the containing flat equals to k 1 + k 2 minus the dimension of the intersection. These two operations (referred to as meet and join ) make the set of all flats in the Euclidean n -space a lattice and can build systematic coordinates for flats in any dimension, leading to Grassmann coordinates or dual Grassmann coordinates. For example,

525-418: The plane itself; the flats in three-dimensional space are points, lines, planes, and the space itself. The definition of flat excludes non-straight curves and non-planar surfaces , which are subspaces having different notions of distance: arc length and geodesic length , respectively. Flats occur in linear algebra , as geometric realizations of solution sets of systems of linear equations . A flat

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550-452: The same dimension either coincide or do not intersect; they can be described by two systems of linear equations which differ only in their right-hand sides. If flats do not intersect, and no line from the first flat is parallel to a line from the second flat, then these are skew flats . It is possible only if sum of their dimensions is less than dimension of the ambient space. For two flats of dimensions k 1 and k 2 there exists

575-444: The same term [REDACTED] This disambiguation page lists articles associated with the title Flat . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Flat&oldid=1250204492 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description

600-444: The same term [REDACTED] This disambiguation page lists articles associated with the title Flat . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Flat&oldid=1250204492 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description

625-510: The shore of Massachusetts, U.S. Kentish Flats Offshore Wind Farm , off the coast of Kent, England Rhyl Flats , a wind farm off the coast of North Wales Flat coast , a shoreline where the land descends gradually into the sea Places [ edit ] United States [ edit ] Flat, Alaska , a census-designated place Flat, Kentucky , an unincorporated community Flat, Missouri , an unincorporated community Flat, Texas , an unincorporated community Flat Brook ,

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