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This means that if the various observations (X 1i, X 2i) are plotted in the (X 1, X 2) plane, these points are collinear in the sense defined earlier in this article. Perfect multicollinearity refers to a situation in which k ( k ≥ 2) explanatory variables in a multiple regression model are perfectly linearly related, according to
(If one of the four points is the line's point at infinity, then the two distances involving that point are dropped from the formula.) The point D is the harmonic conjugate of C with respect to A and B precisely if the cross-ratio of the quadruple is −1 , called the harmonic ratio .
The Simson line LN (red) of the triangle ABC with respect to point P on the circumcircle. In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. [1] The line through these points is the Simson line of P, named for Robert Simson. [2]
Thus (E, H; J, G) = (E, K; D, L), so by Lemma X, the points H, M, and K are collinear. That is, the points of intersection of the pairs of opposite sides of the hexagon ADEGBZ are collinear. Lemmas XV and XVII are that, if the point M is determined as the intersection of HK and BG, then the points A, M, and D are collinear.
Simply, a collineation is a one-to-one map from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. One may formalize this using various ways of presenting a projective space. Also, the case of the projective line is special, and hence generally treated ...
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: Given three collinear points A, B, C , let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively.
These subsets subdivide the plane into shapes of the following three types: [1] The cells or chambers of the arrangement are two-dimensional regions not part of any line. They form the interiors of bounded convex polygons or unbounded convex regions. These are the connected components of the points that would remain after removing all points on ...
A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a collineation or symmetry of the plane. The collineations of a geometry form a group under composition, and for the Fano plane this group (PΓL(3, 2) = PGL(3, 2)) has 168 elements.