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In geometry, collinearity of a set of points is the property of their lying on a single line. [1] A set of points with this property is said to be collinear (sometimes spelled as colinear [ 2 ] ). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
Möbius' designation can be expressed by saying, collinear points are mapped by a permutation to collinear points, or in plain speech, straight lines stay straight. Contemporary mathematicians view geometry as an incidence structure with an automorphism group consisting of mappings of the underlying space that preserve incidence. Such a mapping ...
Let x, y, and z refer to a coordinate system with the x- and y-axis in the sensor plane. Denote the coordinates of the point P on the object by ,,, the coordinates of the image point of P on the sensor plane by x and y and the coordinates of the projection (optical) centre by ,,.
It is essentially the only projective invariant of a quadruple of collinear points; this underlies its importance for projective geometry. The cross-ratio had been defined in deep antiquity, possibly already by Euclid , and was considered by Pappus , who noted its key invariance property.
The maximum distance (as measured in the collinearity graph) between two points is d, and; For every point X and line l there is a unique point on l that is closest to X. A near 0-gon is a point, while a near 2-gon is a line. The collinearity graph of a near 2-gon is a complete graph. A near 4-gon is a generalized quadrangle (possibly degenerate).
However, because income is equal to expenses plus savings by definition, it is incorrect to include all 3 variables in a regression simultaneously. Similarly, including a dummy variable for every category (e.g., summer, autumn, winter, and spring) as well as an intercept term will result in perfect collinearity. This is known as the dummy ...
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings.
In geometry, lines in a plane or ... In projective geometry, in two dimensions concurrency is the dual of collinearity; in three dimensions, concurrency is the dual ...