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Coplanarity. In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
e. In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting" [ 1 ][ 2 ]) the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines.
Origins from Alice's and Bob's perspectives. Vector computation from Alice's perspective is in red, whereas that from Bob's is in blue. The following characterization may be easier to understand than the usual formal definition: an affine space is what is left of a vector space after one has forgotten which point is the origin (or, in the words of the French mathematician Marcel Berger, "An ...
Look up collinearity or collinear in Wiktionary, the free dictionary. 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 ...
Skew lines. Rectangular parallelepiped. The line through segment AD and the line through segment B 1 B are skew lines because they are not in the same plane. In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of ...
The following are the assumptions of the point-line-plane postulate: [ 1 ] Unique line assumption. There is exactly one line passing through two distinct points. Number line assumption. Every line is a set of points which can be put into a one-to-one correspondence with the real numbers. Any point can correspond with 0 (zero) and any other ...
For a set P of points in the (d -dimensional) Euclidean space, a Delaunay triangulation is a triangulation DT (P) such that no point in P is inside the circum-hypersphere of any d - simplex in DT (P). It is known [ 2 ] that there exists a unique Delaunay triangulation for P if P is a set of points in general position; that is, the affine hull ...
Lami's theorem. In physics, Lami 's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors. According to the theorem, {\displaystyle {\frac {v_ {A}} {\sin \alpha }}= {\frac {v_ {B}} {\sin ...