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collinearity
In geometry, collinearity is a property of a set of points, specifically, the property of lying on a single line.〔The concept applies in any geometry , but is often only defined within the discussion of a specific geometry , 〕 A set of points with this property is said to be collinear (sometimes spelled as colinear〔(Colinear (Merriam-Webster dictionary) )〕). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
==Points on a line==
In any geometry, the set of points on a line are said to be collinear. In Euclidean geometry this relation is intuitively visualized by points lying in a row on a "straight line". However, in most geometries (including Euclidean) a line is typically a primitive (undefined) object type, so such visualizations will not necessarily be appropriate. A model for the geometry offers an interpretation of how the points, lines and other object types relate to one another and a notion such as collinearity must be interpreted within the context of that model. For instance, in spherical geometry, where lines are represented in the standard model by great circles of a sphere, sets of collinear points lie on the same great circle. Such points do not lie on a "straight line" in the Euclidean sense, and are not thought of as being ''in a row''.
A mapping of a geometry to itself which sends lines to lines is called a collineation, it preserves the collinearity property.
The linear maps (or linear functions) of vector spaces, viewed as geometric maps, map lines to lines, that is, they map collinear point sets to collinear point sets and so, are collineations. In projective geometry these linear mappings are called ''homographies'' and are just one type of collineation.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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