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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. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    The Cartesian coordinates of a point are usually written in parentheses and separated by commas, as in (10, 5) or (3, 5, 7). The origin is often labelled with the capital letter O. In analytic geometry, unknown or generic coordinates are often denoted by the letters (x, y) in the plane, and (x, y, z) in three-dimensional space. This custom ...

  5. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Points with equal power, isolines of (), are circles concentric to circle . Steiner used the power of a point for proofs of several statements on circles, for example: Determination of a circle, that intersects four circles by the same angle. [2] Solving the Problem of Apollonius

  6. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. [16] In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as ...

  7. 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).

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