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  2. Point (geometry) - Wikipedia

    en.wikipedia.org/wiki/Point_(geometry)

    In geometry, a point is an abstract idealization of an exact position, without size, in physical space, [1] or its generalization to other kinds of mathematical spaces.As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist; conversely ...

  3. List of mathematical properties of points - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    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 ...

  4. Point group - Wikipedia

    en.wikipedia.org/wiki/Point_group

    In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d).

  5. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .

  6. Geometry - Wikipedia

    en.wikipedia.org/wiki/Geometry

    Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...

  7. Point at infinity - Wikipedia

    en.wikipedia.org/wiki/Point_at_infinity

    The real line with the point at infinity; it is called the real projective line. In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane.

  8. Point - Wikipedia

    en.wikipedia.org/wiki/Point

    Point (geometry), an entity that has a location in space or on a plane, but has no extent; more generally, an element of some abstract topological space Point, or Element (category theory), generalizes the set-theoretic concept of an element of a set to an object of any category

  9. Finite geometry - Wikipedia

    en.wikipedia.org/wiki/Finite_geometry

    A projective plane geometry is a nonempty set X (whose elements are called "points"), along with a nonempty collection L of subsets of X (whose elements are called "lines"), such that: For every two distinct points, there is exactly one line that contains both points. The intersection of any two distinct lines contains exactly one point.