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Antipodal point, the point diametrically opposite to another point on a sphere, such that a line drawn between them passes through the centre of the sphere and forms a true diameter; Conjugate point, any point that can almost be joined to another by a 1-parameter family of geodesics (e.g., the antipodes of a sphere, which are linkable by any ...
Let L = (P, G, I) be an incidence structure, for which the elements of P are called points and the elements of G are called lines. L is a linear space if the following three axioms hold: (L1) two distinct points are incident with exactly one line. (L2) every line is incident to at least two distinct points. (L3) L contains at least two distinct ...
Example 1: points and lines of the Euclidean plane (top) Example 2: points and circles (middle), Example 3: finite incidence structure defined by an incidence matrix (bottom) In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects.
Given a point and a line, there is a unique line which contains the point and is parallel to the line. Parallelism is an equivalence relation on the lines of an affine plane. Since no concepts other than those involving the relationship between points and lines are involved in the axioms, an affine plane is an object of study belonging to ...
An incidence structure = (,,) consists of a set of points, a set of lines, and an incidence relation, or set of flags, ; a point is said to be incident with a line if (,) . It is a ( finite ) partial geometry if there are integers s , t , α ≥ 1 {\displaystyle s,t,\alpha \geq 1} such that:
A complete quadrangle (at left) and a complete quadrilateral (at right).. In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.