kollineare

Kollineare is a term used in geometry to describe entities that lie on a single straight line. The word is commonly used to describe sets of points, and by extension vectors or lines, that share a common line.

Formally, a set of points A, B, C is kollineare if there exists a line L such that A, B, and C all lie on L. In the plane, three points are kollineare if the area of triangle ABC is zero. Equivalently, the determinant formed by their coordinates, or the cross-product of vectors AB and AC, vanishes. In higher dimensions, a set of points is kollineare if all points lie on the same line, which can be described parametrically as P(t) = A + t v for some fixed point A and direction vector v.

Kollineare extends to lines and vectors as a broader concept of alignment. This notion is central to tests for collinearity in computational geometry, graphics, and linear algebra. It is also used to distinguish line-based configurations from non-collinear ones, such as the vertices of a triangle or polygon that do not lie on a single line.

See also: Collinearity, Linear algebra, Determinant, Affine geometry.